Cellular structures with twelve-cornered cells

ABSTRACT

A structural component includes at least one wall surrounding a component interior space. The structural component also includes a first cellular structure positioned within the component interior space. The first cellular structure includes a plurality of cells each having a twelve-cornered cross section including twelve sides and twelve corners creating nine internal angles and three external angles.

This application is divisional of U.S. Utility patent application Ser.No. 15/138,466, filed Apr. 26, 2016, which is an application related toU.S. Utility patent application Ser. No. 15/138,465, entitled “CELLULARSTRUCTURES WITH TWELVE-CORNERED CELLS,” filed Apr. 26, 2016; to U.S.Design patent application Ser. No. 29/562,441, entitled “CELLULARSTRUCTURE,” filed Apr. 26, 2016; to U.S. Design patent application Ser.No. 29/562,443, entitled “CELLULAR STRUCTURE,” filed Apr. 26, 2016; toU.S. Design patent application Ser. No. 29/562,442, entitled “REPEATINGCELLULAR PATTERN,” filed Apr. 26, 2016; and to U.S. Design patentapplication Ser. No. 29/562,439, entitled “REPEATING CELLULAR PATTERN,”filed Apr. 26, 2016, the entire contents of each of which areincorporated by reference herein.

TECHNICAL FIELD

The present disclosure relates generally to a cellular structure for astructural component. The present disclosure relates more specificallyto a cellular structure having a plurality of cells, each cell having across section formed by twelve sides and twelve corners.

BACKGROUND

It is desirable for a structural component to maximize impact energyabsorption and bending resistance while minimizing mass per unit lengthof the structural component. When a compressive force is exerted on astructural component (e.g., a force from a collision, explosion,projectile, etc.), the structural component can crush and/or bend in adimensional direction (e.g., longitudinal direction or lateraldirection) to absorb the energy of the force. Compressive force energyabsorption may be maximized, for example, by assuring that thestructural component compacts substantially along a dimensional axis(e.g., longitudinal axis or lateral axis) of the structural componentupon experiencing an impact along this axis. Such compaction may bereferred to as a stable axial crush of the structural component.

Conventional structural components rely on interior cellular structureswith multiple cells that each have a cross section with a basicpolygonal shape to improve compressive energy absorption and crushstability. Most often cells having a cross section with a hexagonalshape are used such that the interior cellular structure mimics that ofa honeycomb. However, while a cellular structure having such cells witha basic polygonal cross section can provide compressive energyabsorption and crush stability for the structural component, such acellular structure increases the weight of the structural component. Itmay be desirable to provide a strengthening assembly configured toachieve the same or similar strength increase as provided by thecellular structure made up of cells having a cross section with a basicpolygonal shape (e.g., triangular, rectangular, pentagonal, hexagonal,heptagonal, or octagonal), while minimizing mass per unit length of thestructural component, and maintaining a high manufacturing feasibility.

It may further be desirable to provide a structural component that canachieve increased energy absorption and a more stable axial collapsewhen forces such as front and side impact forces are exerted on thestructural component, while also conserving mass to minimize the totalweight of a structure. Where the structure that the structural componentis a part of is a vehicle, such mass conservation can aid in meetingvehicle fuel efficiency and emission requirements. Also, it may bedesirable to provide a structural component that can achieve improvedenergy absorption and bend when a bending force is exerted on thestructural component. In addition, it may be desirable, to provide atunable cross section for cells within the cellular structure that isconfigured to achieve strength increases (i.e., load carrying andcompression energy absorption) over basic polygonal designs, while alsoallowing flexibility in design to meet a range of applications specificto the structure that the structural component is a part of.

SUMMARY

In accordance with various exemplary embodiments of the presentdisclosure, a cellular structure is provided. The cellular structureincludes a plurality of cells each having a twelve-cornered crosssection. The twelve-cornered cross section includes twelve straightsides and twelve corners creating nine internal angles and threeexternal angles.

In accordance with another aspect of the present disclosure, astructural component is provided. The structural component includes atleast one wall surrounding a component interior space; and a cellularstructure positioned within the interior space. The cellular structureincludes a plurality of cells each having a twelve-cornered crosssection. The twelve-cornered cross section includes twelve sides andtwelve corners creating nine internal angles and three external angles.

In accordance with another aspect of the present disclosure, a cellularstructure including at least two cells is provided. Each cell includes aplurality of longitudinal walls extending between a top and a bottom ofthe cell, the longitudinal walls intersecting to create corners of thecell. Further, a transverse cross section of each cell comprisesinternal angles and external angles, wherein each of at least three ofthe internal angles and at least one of the external angles issubstantially the same.

In accordance with another aspect of the present disclosure, a sandwichstructure is provided. The sandwich structure includes first and secondplanar structures, and a cellular structure positioned between the firstand second planar structures. The cellular structure includes at leasttwo cells. Each cell includes a plurality of longitudinal wallsextending between a top and a bottom of the cell, the longitudinal wallsintersecting to create corners of the cell, wherein a transverse crosssection of the cell comprises at least two bisecting planes of symmetry.

Additional objects and advantages will be set forth in part in thedescription which follows, and in part will be obvious from thedescription, or may be learned by practice of the present teachings. Theobjects and advantages of the present disclosure will be realized andattained by means of the elements and combinations particularly pointedout in the appended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the claimed subject matter. The accompanyingdrawings, which are incorporated in and constitute part of thisspecification, illustrate exemplary embodiments of the presentdisclosure and together with the description, serve to explainprinciples of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

At least some features and advantages of the present teachings will beapparent from the following detailed description of exemplaryembodiments consistent therewith, which description should be consideredwith reference to the accompanying drawings, wherein:

FIGS. 1A-1B illustrates a detailed cross-sectional and perspectiveviews, respectively, of an exemplary twelve-cornered cell of anexemplary cellular structure in accordance with the present disclosure;

FIGS. 2A-2B illustrate detailed perspective and top views, respectively,of a first exemplary embodiment of a structural component having acellular structure formed by a plurality of cells, each full cell havingthe exemplary twelve-cornered cross section, as shown in FIGS. 1A-1B;

FIG. 3 illustrates a detailed cross section of another exemplarytwelve-cornered cell of another exemplary cellular structure inaccordance with the present disclosure;

FIG. 4 illustrates a top view of a second exemplary embodiment of astructural component having a cellular structure with a plurality ofcells, each full cell having the exemplary twelve-cornered crosssection, as shown in FIG. 3;

FIG. 5A illustrates a detailed top view of a structural component havinga cellular structure with a plurality of cells, each full cell having abasic, four-cornered cross section;

FIG. 5B illustrates a detailed top view of a structural component havinga cellular structure with a plurality of cells, each full cell having abasic, six-cornered cross section;

FIG. 5C illustrates another detailed top view of the exemplarystructural component of FIGS. 2A-2B;

FIG. 6A illustrates a detailed perspective view of the structuralcomponent of FIG. 5A.

FIG. 6B illustrates a detailed perspective view of the structuralcomponent of FIG. 5B.

FIG. 6C illustrates a detailed perspective view of the structuralcomponent of FIG. 5C.

FIGS. 7A-7C illustrate modeled aluminum versions of the structuralcomponents shown in FIGS. 6A-6C, respectively, at a time interval of 8milliseconds during an exemplary dynamic crush;

FIG. 8 is a graph of normalized dynamic crush force and associated crushdisplacement for modeled aluminum versions of the structural componentsshown in FIGS. 6A-6C;

FIG. 9 is a graph of normalized dynamic axial crush energy absorbed andassociated axial crush displacement for the exemplary modeled aluminumversions of the structural components shown in FIGS. 6A-6C;

FIG. 10 is a graph of normalized quasi-static crush force and associatedcrush displacement for modeled aluminum versions of the structuralcomponents shown in FIGS. 6A-6C;

FIG. 11A-11C illustrates modeled polymer versions of the structuralcomponents shown in FIGS. 6A-6C, respectively, at a time intervals of 8milliseconds during an exemplary dynamic crush;

FIG. 12 is a graph of normalized dynamic crush force and associatedcrush displacement for modeled polymer versions of the structuralcomponents shown in FIGS. 6A-6C;

FIG. 13 is a graph of normalized dynamic axial crush energy absorbed andassociated axial crush displacement for the exemplary modeled polymerversions of the structural components shown in FIGS. 6A-6C;

FIG. 14 is a graph of normalized quasi-static crush force and associatedcrush displacement for modeled polymer versions of the structuralcomponents shown in FIGS. 6A-6C;

FIGS. 15A and 15B illustrate modeled aluminum versions of variousstructural components with either a square-celled ortwelve-corner-celled cellular structure, at time intervals of 0milliseconds and 8 milliseconds during an exemplary dynamic crush,respectively;

FIG. 16 is a graph of dynamic crush force and associated crushdisplacement for modeled aluminum versions of the structural componentsshown in FIG. 15A;

FIG. 17 is a graph of dynamic axial crush energy absorbed and associatedaxial crush displacement for the exemplary modeled aluminum versions ofthe structural components shown in FIG. 15A;

FIGS. 18A and 18B illustrate modeled polymer versions of variousstructural components with either a square-celled ortwelve-corner-celled cellular structure, at time intervals of 0milliseconds and 8 milliseconds during an exemplary dynamic crush,respectively;

FIG. 19 is a graph of dynamic crush force and associated crushdisplacement for modeled polymer versions of the structural componentsshown in FIG. 18A;

FIG. 20 is a graph of dynamic axial crush energy absorbed and associatedaxial crush displacement for the exemplary modeled polymer versions ofthe structural components shown in FIG. 18A;

FIGS. 21A and 21B illustrate modeled aluminum versions of variousstructural components with either a hexagon-celled ortwelve-corner-celled cellular structure, at time intervals of 0milliseconds and 8 milliseconds during an exemplary dynamic crush,respectively;

FIG. 22 is a graph of dynamic crush force and associated crushdisplacement for modeled aluminum versions of the structural componentsshown in FIG. 21A;

FIG. 23 is a graph of dynamic axial crush energy absorbed and associatedaxial crush displacement for the exemplary modeled aluminum versions ofthe structural components shown in FIG. 21A;

FIGS. 24A and 24B illustrate modeled polymer versions of variousstructural components with either a hexagon-celled ortwelve-corner-celled cellular structure, at time intervals of 0milliseconds and 8 milliseconds during an exemplary dynamic crush,respectively;

FIG. 25 is a graph of dynamic crush force and associated crushdisplacement for modeled polymer versions of the structural componentsshown in FIG. 24A;

FIG. 26 is a graph of dynamic axial crush energy absorbed and associatedaxial crush displacement for the exemplary modeled polymer versions ofthe structural components shown in FIG. 24A;

FIG. 27 illustrates an exemplary embodiment of a vehicle frame withseveral components for which a cellular structure in accordance with thepresent teachings can be used;

FIG. 28 illustrates an exemplary embodiment of a vehicle upper body withseveral components for which a cellular structure in accordance with thepresent teachings can be used;

FIG. 29A illustrates a perspective view of an exemplary embodiment of asandwich structure having a cellular structure with a plurality ofcells, each full cell having an exemplary twelve-cornered cross sectionin accordance with the present teachings;

FIG. 29B illustrates a perspective cutaway view of the exemplaryembodiment of a sandwich structure shown in FIG. 29A; and

FIG. 30 illustrates a detailed perspective view a third exemplaryembodiment of a structural component having a cellular structure with aplurality of cells, each full cell having the exemplary twelve-corneredcross section, as shown in FIG. 1.

Although the following detailed description makes reference to exemplaryillustrative embodiments, many alternatives, modifications, andvariations thereof will be apparent to those skilled in the art.Accordingly, it is intended that the claimed subject matter be viewedbroadly.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Reference will now be made in detail to various exemplary embodiments,examples of which are illustrated in the accompanying drawings. Thevarious exemplary embodiments are not intended to limit the disclosure.To the contrary, the disclosure is intended to cover alternatives,modifications, and equivalents of the exemplary embodiments. In thedrawings and the description, similar elements are provided with similarreference numerals. It is to be noted that the features explainedindividually in the description can be mutually combined in anytechnically expedient manner and disclose additional embodiments of thepresent disclosure.

This description's terminology is not intended to limit the invention.For example, spatially relative terms—such as “beneath”, “below”,“lower”, “above”, “upper”, “proximal”, “distal”, “front”, “rear”,“left”, “right”, “horizontal”, “vertical”, and the like—may be used todescribe one element's or feature's relationship to another element orfeature as illustrated in the figures. These spatially relative termsare intended to encompass different positions (i.e., locations) andorientations (i.e., rotational placements) of a device in use oroperation in addition to the position and orientation shown in thefigures. For example, if a device in the figures is turned over,elements described as “below” or “beneath” other elements or featureswould then be “above” or “over” the other elements or features. Thus,the exemplary term “below” can encompass both positions and orientationsof above and below. A device may be otherwise oriented (rotated 90degrees or at other orientations) and the spatially relative descriptorsused herein interpreted accordingly. In the orientation of the figuresin the application, relative x-axis, y-axis, and z-axis directions ofthe devices have been labeled.

The present disclosure contemplates cellular structures for a structuralcomponent, particularly, an interior of a structural component. Thecellular structures of this disclosure are configured to achieve thesame or similar strength increase as provided by a cellular structuremade up of cells having a cross section with a basic polygonal shape(e.g., triangular, rectangular, pentagonal, hexagonal, heptagonal, oroctagonal), while minimizing mass per unit length of the structuralcomponent. The present disclosure relates more specifically to acellular structure having a plurality of cells, each cell having a crosssection formed by twelve straight sides and twelve corners. The crosssectional shapes of the cells of the cellular structures of the presentdisclosure are designed based in part on, for example, a variety oftunable parameters configured to achieve strength increases (i.e., loadcarrying and energy absorption) over basic polygonal designs (e.g.,polygonal cellular cross sections having less or the same number ofsides), while also allowing design flexibility to meet a range ofapplications specific to the structure that the structural component isa part of.

The twelve sides and twelve corners of a cross section of a cell maycreate eight internal angle and four external angles. A cellularstructure in accordance with the present disclosure may include aplurality of such cells. The plurality of cells may or may not beinterconnected. The cellular structure may include a plurality of fullcells each having twelve sides and twelve corners, as described above.Alternatively, a cellular structure may include a combination of aplurality of full cells and a plurality of partial cells.

In accordance with the present teachings, the shape of the cells of thecellular structures of the structural components disclosed hereinprovides the cellular structures as well as the overall structuralcomponents with stabilized folding, reduced crush distance, andincreased energy absorption in response to an applied compression force.

Additionally or alternatively, incorporation of the cellular structuresof the present disclosure within a structural component can allow foruse of a structural component having an outer periphery formed in abasic polygonal shape, such as a circular, oval, triangle, square, orrectangle, the structural component thus having a cross section, in abasic polygonal shape. Thus, rather than relying on a structuralcomponent having an outer periphery formed into a complex shape (e.g., astructural component having more than four sides) to provide increasedstrength and/or minimized mass per unit length of the structuralcomponent, a cellular structure according to the present disclosure maybe incorporated into an interior of a structural component having across section with a basic polygonal shape such that the interior of thestructural component is at least partially filled with the cellularstructure, which provides increased strength and/or minimized mass perunit length of the structural component. Alternatively, it is alsocontemplated that a cellular structure according to the presentdisclosure may be incorporated into an interior of a structuralcomponent having an outer periphery in a complex shape, for example acomplex polygonal shape.

In some exemplary embodiments, some or all of the cells of an exemplarycellular structure may be partially or wholly filled with variousfillers. Further, more than one cellular structure may be provided, andwith some or all of one or more of the cellular structures having someor all of the cells of the given structure being partially or whollyfilled with one or more types of fillers. For example, where temperaturecontrol is desired, some or all of the cells may be partially or whollyfilled with thermally insulating filler(s). Exemplary thermallyinsulating fillers include various foams (e.g., blown fiber glass foam,polyurethane foams), mineral wool, cellulose, polystyrene aerogels,cork, and combinations thereof. Additionally or alternatively, in othervarious exemplary embodiments, where sound control is required, some orall of the cells of the exemplary cellular structure(s) may be partiallyor wholly filled with noise insulating filler(s). Exemplary noiseinsulating fillers include sponge(s) melamine acoustic foams, mineralwool, open-cell rubber foams, and combinations thereof. In furthervarious exemplary embodiments, where further structural reinforcement isdesired, the cells may be partially or wholly filled with strengtheningfiller(s). Exemplary strengthening fillers include structural foam(s),such as thermoplastic structural foams, aluminum foams, glass or carbonfiber-reinforced structural foams, closed-cell polymer foams, andcombinations thereof. In some exemplary embodiments, more than one typeof filler may be incorporated in the cells. In some other exemplaryembodiments, a filler may provide more than one, or even all, of thethermally insulating, noise insulating, and strengthening functions andmay partially or wholly fill some or all of the cells of the exemplarycellular structure(s). Alternatively, some or all of the cells may beleft unfilled (i.e., hollow or empty).

The cellular structures made up of cells having a twelve-cornered crosssection as disclosed herein, and the structural components that containone or more such cellular structures, in accordance with the presentdisclosure, can achieve increased energy absorption and a more stableaxial collapse in comparison to cellular structures formed by cellshaving differing numbers of corners or sides and structural componentswithout cellular structures or containing cellular structure(s) formedby cells having differing numbers of corners or sides, when forces suchas front and side compression forces are exerted on the cellularstructure and/or structural component. Furthermore, the twelve-corneredcross section of the cells of the cellular structures and structuralcomponents containing cellular structures formed of cells having thetwelve-cornered cross section in accordance with the present disclosurecan achieve a similar, if not greater, strength increase than cellularstructures formed of cells having a hexagonal cross section (e.g.,honeycomb cellular structures) and structural components containinghoneycomb cellular structure(s), while minimizing mass per unit lengthof the cellular structures and structural components, and maintaining ahigh manufacturing feasibility because the structural component and/orthe cellular structure with twelve-cornered cells thereof can be formedby stamping, bending, press forming, hydro-forming, molding, casting,extrusion, uniform or non-uniform roll forming, machining, forging, 3Dprinting, and/or other known manufacturing processes. In particular,extrusion and/or molding may be used to form cellular structures with alarge number of cells and/or high volume production. Thus-formedcomponents or sections of components can be joined via welding (e.g.,spot welding, seam welding, laser welding, and friction stir welding),brazing, soldering, adhesive bonding, fastening, press fitting,riveting, screwing, bolting, and/or other known joining technologies.

For cellular structures that are relatively large and with only smallnumber of cells, each cell may be manufactured by other processesseparately and then joined together thereafter. Any of theaforementioned manufacturing and joining methods may be used to formsuch cellular structures which are relatively large and with only smallnumber of cells. Furthermore, any of the aforementioned processes may beused for low volume production, for example, where a specificallytailored cellular structure is required. In addition, casting may beused to form magnesium and aluminum structural components with cellularstructure(s) incorporated therein.

The cellular structure formed by cells having twelve corners, andstructural components containing such cellular structures in accordancewith the present teachings can be made of, for example, steel alloys,titanium alloys, aluminum alloys, magnesium alloys, nylons, plastics,polymers, composites, fiber-reinforced composites, silicone,semiconductor, papers, rubber, foams, gels, woods, corks, hybridmaterials (i.e., multiple dissimilar materials), shape-memory materials,and/or any other suitable materials. Those of ordinary skill in the artwould understand, for example, that the material used for a structuralcomponent and cellular structure thereof may be chosen based at least inpart on intended application, strength/weight considerations, cost,packaging space, and/or other design factors.

Although discussed herein primarily with respect to automotiveapplications, the present disclosure contemplates that the variousstructural components and cellular structures disclosed herein may besuitable for many applications in many fields, including, for example,the fields of aeronautics (e.g., aircraft, spacecraft, etc.),watercrafts (e.g., paneling, body shell structures, interior furniture,etc. of a watercraft), railway vehicles, tram vehicles, high speed railvehicles, magnetic levitation vehicles, and hyperloop capsules orvehicles, shipping and packaging (e.g., shipping box, pallet, cushioningmember, etc.), structural vessel design (e.g., fuselage structures,water vessels, air vessels, locomotives, etc.), turbine design (e.g.,rotor blade design of an engine turbine or wind turbine), solar energy(e.g., solar panel design), sporting equipment (e.g., skis, snowboards,surfboards, wakeboards, paddle boards, skateboards, water paddles, pingpong paddles, pickle ball paddles, baseball and softball bases, paddingfor contact sport pads, helmets, helmet padding, gloves, motor sportbody armors, etc.), foot wear (e.g., shoes, athletic shoes, sandals,slippers, socks, etc. and inserts, inner soles, outer soles and upperexteriors thereof), bedding or other furniture cushioning (e.g.,mattress layers, mattress pads, pillows, blankets, cushions, etc.),protective cases for mobile devices (e.g. cellular phones, tablets,media players, digital cameras, cameras, etc.), furniture (e.g., tables,stools, and chairs), shelving, storage (e.g. storage bins, tool boxes,travel cases, carrying cases, etc.), insulation (e.g., thermalinsulation and sound absorption structures), construction materials(e.g., for wall structures, floor structures, roof structures, ceilingstructures of buildings, as well as building surface coverings such aslaminates or padding), and other strengthening applications notspecifically listed here. This list of potential applications for thestructures disclosed herein is intended to be exemplary only, and is notintended to limit or exclude other applications not listed herein.

Turning now to the drawings, an exemplary embodiment of a single cell100 of a cellular structure in accordance with the present disclosure isillustrated in FIGS. 1A and 1B, which shows detailed cross-sectional andperspective views, respectively of the single cell 100 of a cellularstructure. The cell 100 has longitudinal walls that meet at longitudinaledges, which define twelve sides 102A-102L and twelve corners, of whichnine are internal corners 104A-104I and three are external corners106A-106C of the twelve-cornered cross section in accordance with thepresent disclosure. Each side 102A-102L has a cross-sectional lengthL₁-L₁₂ and cross-sectional thicknesses T₁-T₁₂, respectively. Eachinternal corner 104A-104I has an internal angle ϑ_(i1)-ϑ_(i9)respectively. Each external corner 106A-106C has an external anglesϑ_(e1)-ϑ_(e3), respectively. As shown in FIG. 1A, each side 102A-102Lmay be straight and each corner may be a sharp corner defined by ameeting point of two adjacent sides. Alternatively, although not shown,sides may be curved at their ends to provide rounded corners.Accordingly, it is contemplated that each corner may be a rounded cornerhaving a bend radius.

Depending upon the particular application and/or the desired features ofthe structural component and/or the cellular structure thereof, thelengths of the sides and the thicknesses of the sides of thetwelve-sided, twelve-cornered cross section of the cells of the cellularstructure can be varied (i.e., can be tuned) to achieve improvedstrength and other performance features (e.g., stability of foldingpattern) compared to basic polygonal cross sections of cells of aconventional cellular structure. Varying these features of thetwelve-sided, twelve-cornered strengthening member may obviate the needfor increased corner thickness. In accordance with various exemplaryembodiments of the present teachings, the cross-sectional lengths L₁-L₁₂of sides 102A-102L and the cross-sectional thicknesses T₁-T₁₂ of thesides 102A-102L can be varied to a certain degree, as would beunderstood by one skilled in the art, for example in accordance withavailable space within a structural component.

The perimeter of the twelve-cornered cell's cross section generallyforms a polygon comprising a plurality of internal and external corners.As embodied herein and shown in FIG. 1A, the polygon may be formed ofalternating internal and external corners/angles, and in particular, maybe formed by alternating three consecutive internal corners/angles witha single external corner/angle. This repeating pattern, which alternatesbetween three consecutive internal corners/angles and one externalcorner angle (i.e., an alternating three-in-one-out configuration),results in a cross section with more than two bisecting planes ofsymmetry (e.g., three bisecting planes of symmetry). For example, cell100 of FIG. 1A has three bisecting planes of symmetry.

Cell 100 with the twelve-cornered cross section shown in FIG. 1A hasnine internal corners 104A-104I and three external corners 106A-106C.More than two bisecting planes of symmetry, as described above, may beprovided when each internal angle ϑ_(i1)-ϑ_(i9) of each internal corner104A-104I is substantially the same and each external angleϑ_(e1)-ϑ_(e3) of each external corner 106A-106C is substantially thesame. In this case, the internal angles ϑ_(i1)-ϑ_(i9) are collectivelyreferred to as internal angle ϑ_(i) and the external anglesϑ_(e1)-ϑ_(e3) are collectively referred to as external angle ϑ_(e). Morethan two bisecting planes of symmetry, as described above, may also beprovided when each of the internal angles ϑ_(i1)-ϑ_(i9) of each internalcorner 104A-104I and each of the external angles ϑ_(e1)-ϑ_(e3) of eachexternal corner 106A-106C is substantially the same. In this case, theinternal angles ϑ_(i1)-ϑ_(i9) and the external angles ϑ_(e1)-ϑ_(e3) arecollectively referred to as corner angle ϑ. FIG. 1A illustrates anexemplary embodiment in which the internal angle ϑ_(i) is approximately120 degrees and the external angle ϑ_(e) is approximately 120 degrees.Thus, FIG. 1A illustrates an exemplary embodiment where both each of thenine internal angles ϑ_(i1)-ϑ_(i9) and three external anglesϑ_(e1)-ϑ_(e3) are substantially the same corner angle ϑ, and, moreparticularly, each of the internal angles and external angles are about120 degrees.

In certain exemplary embodiments of the present disclosure, such as inan automobile, board sport, packaging, furniture, turbine, or solarapplication, for example, a cross-sectional length L₁-L₁₂ of each side102A-102L of the each of the cells 100 can range from about 2 mm toabout 50 mm. In other exemplary embodiments, such as in an aircraft,spacecraft, watercraft, wind turbine, or building application, forexample, a length of each side L₁-L₁₂ of the strengthening member may belarger. In yet other exemplary embodiments, such as, for example, someultra-light spacecraft applications, a length of each side L₁-L₁₂ of thestrengthening member may be smaller, for example, nanoscopic in scale.In some exemplary embodiments the cross-sectional lengths L₁-L₁₂ of eachside (e.g., each side 102A-102L (see FIG. 1)) is substantially the same.Furthermore, in some other exemplary embodiments the cross-sectionallengths L₁-L₁₂ of each side can vary with respect to the cross-sectionallength of one or more of each other side wall (e.g., cell 300 of FIGS. 3and 4). Alternatively or additionally, in some exemplary embodiments,the cross-sectional length of a side can vary along a length of thelongitudinal side of the cell (i.e., the longitudinal wall of the celltapers along its length such that the cross-sectional lengths vary toform the taper).

In certain exemplary embodiments of the present disclosure, such as in avehicle, board sport, packaging, turbine, or solar application, forexample, a cross-sectional thickness T₁-T₁₂ of each side 102A-102L ofthe each of the cells 100 can range from about 0.5 mm to about 10 mm. Inother exemplary embodiments of the cells of a cellular structure of astructural component, such as in an aircraft, spacecraft, watercraft,wind turbine, or building application, for example, a thickness T₁-T₁₂of the sides of the strengthening member may be larger. In yet otherexemplary embodiments, such as, for example, ultra-light spacecraftapplications, a thickness T₁-T₁₂ of the sides of the strengtheningmember may be smaller, for example, nanoscopic in scale. In someexemplary embodiments the cross-sectional thickness T₁-T₁₂ of each side(e.g., each side 102A-102L (see FIG. 1)) is substantially the same. Insome other exemplary embodiments the cross-sectional thickness T₁-T₁₂ ofeach side can vary with respect to the cross-sectional thickness of oneor more of the other side walls. Alternatively or additionally, thethickness T₁-T₁₂ can vary within each cross-sectional length of each ofside.

The cross-sectional length and thickness of each side of the cells of acellular structure in accordance with the present disclosure may besized in relation to one another. For example, a ratio of thecross-sectional thickness of a side to the length of the side may rangefrom about 1:4 to about 1:10,000. In the exemplary embodiment of FIG. 1,where the each of the sides 102A-102L has the same cross-sectionallength (i.e., L₁-L₁₂=L) and cross-sectional thickness (i.e., T₁-T₁₂=T),a ratio of the cross-sectional thickness T of the sides 102A-102L to thecross-sectional length L of the sides 102A-102L (i.e., T:L ratio) mayrange from about 1:4 to about 1:10,000.

Referring now to FIG. 30, a detailed perspective view of an exemplaryembodiment of a cellular structure 3000 is shown. The cellular structure3000 includes at least two cells 100, each cell 100 having a pluralityof longitudinal walls that extend between a top and a bottom of thecell. The longitudinal walls intersect to create corners of each cell100, and a transverse cross section of each cell 100 includes twelvecorners. The at least two cells 100 may share one or more longitudinalwalls. For example, the cells may be interconnected such that each cellshares at least one wall with an adjacent cell or some cells, surroundedby others of the plurality of cells, may share each wall with anotheradjacent cell. Additionally or alternatively, each cell may be formedcompletely independently of the other cells in the cellular structure.Furthermore, each cell may have a twelve-cornered transverse crosssection in accordance with the exemplary embodiments shown in FIGS. 1and 3, and/or the descriptions thereof, as set forth herein.Accordingly, the intersections of the longitudinal walls of the cellularstructure 3000 create nine internal angles and three external angles ofeach cell 100. Specifically, each cell 100 of the cellular structure3000 includes twelve longitudinal walls. In various embodiments, such asthat shown in FIG. 30, for example, each side and/or surface of acellular structure is exposed (i.e., free of a panel, wall, or othertype of cover structure), such that the cellular structure itself is astand-alone structural component.

In another exemplary embodiment, illustrated in FIG. 2A, a structuralcomponent 200 includes a cellular structure 201. A cross section of theinterior of structural component 200 is entirely filled with a cellularstructure 201 made up of a plurality of hollow interconnected cells 100with a twelve-cornered cross section and fragments (partial cells)thereof. The cellular structure 100 may extend along a full length ofthe structural component 200 or may extend only along a portion of thelength of the structural component. Additionally or alternatively, aplurality of cellular structures 201 may be provided in the structuralcomponent 200, for example, stacked one on top of another to fill alength of the structural component 200. Additionally or alternatively,as previously discussed, a portion of one or more of the cellularstructures 201 may contain at least some type of filling to provideinsulation against sound and/or heat and/or to add additional strength.Further, although not shown, it is contemplated that the interior of astructural component may be only partially filled with a cellularstructure made up of interconnected cells 100 with a twelve-corneredcross section (e.g., at least a portion of one of a width, depth, orheight (length) of the structural component may not contact a portion ofone or more cellular structures contained within the structuralcomponent).

In various exemplary embodiments, the internal cross section of thestructural component 200 is defined by at least one side or surfaceforming the outer periphery of the structural component. For example,the outer periphery of the structural component may include at least onepanel, wall, or other type of cover structure. The panel, wall, or othertype of cover structure may be opaque or, alternatively, wholly orpartially translucent or transparent so as to make the cellularstructure optically viewable from the exterior of the structuralcomponent. Alternatively, or in addition, to the at least one panel,wall, or other type of cover structure, the structural component mayhave at least side or surface that is open (i.e., free of a panel, wall,or other type of cover structure). For example, the structural component200 of FIG. 2A has six sides, including an upper side that is open anddefined by the upper lateral edges 205 of the cells 100 of the cellularstructure, a lower side (hidden from view in FIG. 2A) that is open anddefined by lower lateral edges (hidden from view in FIG. 2A) of theinterconnected cells 100 of the cellular structure, a front side definedby a front wall 210 (the exterior surface thereof being exposed in FIG.2A), a rear side defined by a rear wall 215 (a portion of the interiorsurface thereof being exposed in FIG. 2A), a left side defined by a leftwall 220 (the exterior surface thereof being exposed in FIG. 2A), and aright side defined by a right wall 225 (a portion of the interiorsurface thereof being exposed in FIG. 2A). The open upper side definedby the upper lateral edges 205 of the cells 100 forms a flat top.Similarly, the open lower side defined by lower lateral edges (hiddenfrom view in FIG. 2A) of the interconnected cells 100 forms a flatbottom. Although not shown, angled and/or curved sides are alsocontemplated.

Referring now to FIG. 2B, a top view of the exemplary structuralcomponent 200 of FIG. 2A is shown. As described above, and shown in FIG.2B, each cell 100 of the cellular structure of the structural component200 has a twelve-cornered cross section with nine internal corners andthree external corners. The internal angle ϑ_(i) of each internal corneris about 120 degrees. The external angle ϑ_(e) of each external corneris about 120 degrees. Additionally, each side of the cells 100 has thesame cross-sectional length and the same cross-sectional thickness.Tuning parameters of the twelve-cornered cross section of each cell inthis manner allows a plurality of the cells to be interconnected suchthat there is no void between any of the twelve cornered cells. In otherwords, all of the full-size cells (i.e., cells that are not cut off by aside or surface of the structural component) with a twelve-corneredcross section are connected together so that there are no gaps oralternatively shaped cells therebetween. In this way, a cellularstructure is provided that consists entirely of connected cells thateach have a twelve-cornered cross section with nine internal cornershaving an internal angle of about 120 degrees and three external cornershaving an internal angle of about 120 degrees. Alternatively, in anotherexemplary embodiment, although not shown, partial cells (i.e.,alternatively shaped cells with a cross section having a differingnumber of total corners or total internal and external corners) that arenot cut off by a side or surface of a structural component may beinterspersed with, and may be connected to, cells in a cellularstructure that includes some cells that have a twelve-cornered crosssection with nine internal corners and three external corners.Additionally or alternatively, a plurality of cellular structures of theabove described varying types may be stacked one on top of another.

For example, an exemplary stacked structure may include a first cellularstructure layer that consists entirely of connected cells that each havea twelve-cornered cross section, and a second cellular structure layerthat includes some cells that have a twelve-cornered cross section andsome alternatively shaped cells. Another exemplary stacked structure mayinclude a first cellular structure layer that consists entirely ofconnected cells that each have a twelve-cornered cross section, and asecond cellular structure layer that consists entirely of connectedcells that each have a twelve-cornered cross section with varieddimensions compared to the cells of the first cellular structure layer.Yet another exemplary stacked structure may include a first cellularstructure layer includes some cells that have a twelve-cornered crosssection and some alternatively shaped cells, and a second cellularstructure layer that includes some cells that have a twelve-corneredcross section and some alternatively shaped cells with varied dimensionscompared to the cells of the first cellular structure layer.

As shown in FIG. 2B, the cells may share longitudinal walls. However,alternatively, each cell may have its own longitudinal walls such thattwo longitudinal walls of adjacent cells form sides that consist of atwo wall barrier between each hollow cell cavity (not shown).

In other various alternative embodiments, for example, a structuralcomponent may have a cellular structure core with two planar structureson opposing sides of the cellular structure so as to form a sandwichstructure. For example, as shown in FIGS. 29A-29B, a sandwich structure2900 can have a cellular structure 2902 between top panel 2904 andbottom panel 2906. Top and bottom panels 2904 and 2906 may be in theform of any type of planar structure. The planar structures may be madeof, for example, paper, wood, aluminum alloys, polymers, and carbon orglass fiber reinforced composites, and may be opaque, translucent,clear, etc. For example, in some applications in which it a sandwichstructure formed from a cellular structure in accordance with thepresent teachings and at least one planar structure, one of the planarstructures may be clear or translucent to allow an observer of theproduct containing the cellular structure to see a portion of thecellular structure, such that the cellular structure forms a part of theaesthetic design of the product. Such a type of product is shown, forexample, in U.S. Patent Application Pub. No. US20080014809, which isincorporated herein by reference. The structure disclosed in U.S. PatentApplication Pub. No. US20080014809 is intended to be exemplary only, andmany other structures can be used as will be understood by to those ofskill in the art.

A cellular structure of the various sandwich structures contemplatedherein includes at least two cells, each cell having a plurality oflongitudinal walls that extend between a top and a bottom of the cell.The longitudinal walls intersect to create corners of the cell, and atransverse cross section of the cell comprises twelve corners.Furthermore, each cell may have a twelve-cornered transverse crosssection in accordance with the exemplary embodiments shown in FIGS. 1and 3, and/or the descriptions thereof, as set forth herein.

Cover structures may be formed integrally with a cellular structure viaconventional means such as molding and/or casting. Alternatively, coverstructures may be bonded, coupled, or otherwise affixed to the cellularstructure via any conventional means, such as adhesion, lamination,mechanical fastening and/or welding.

Referring now to FIG. 3 another exemplary embodiment of a single cell300 of a cellular structure in accordance with the present disclosure isillustrated in FIG. 3, which shows a detailed cross-sectional view ofthe single cell 300 of a cellular structure. Similar to cell 100, thecell 300 has longitudinal walls that meet at longitudinal edges, whichdefine twelve sides 302A-302L and twelve corners, of which nine areinternal corners 304A-304I and three are external corners 306A-306C, ofthe twelve-cornered cross section in accordance with the presentdisclosure. Each side 302A-302L has a cross-sectional length L₁-L₁₂ andcross-sectional thicknesses T₁-T₁₂, respectively. Each internal corner304A-304I has an internal angle ϑ_(i1)-ϑ_(i9), respectively. Eachexternal corner 306A-306C has an external angle ϑ_(e1)-ϑ_(e3),respectively. As shown in FIG. 3, each side may be straight and eachcorner may be a sharp corner defined by a meeting point of two adjacentsides. Alternatively, although not shown, it is contemplated that eachcorner may be a rounded corner having a bend radius and each adjacentstraight side may extend from opposing ends of the rounded corner.

Rather than keeping all of the internal angles ϑ_(i1)-ϑ_(i9) andexternal angles ϑ_(e1)-ϑ_(e3) substantially the same, the internalangles ϑ_(i1)-ϑ_(i9) and external angles ϑ_(e1)-ϑ_(e3) of each corner ofthe cells of a cellular structure in accordance with the presentdisclosure may be sized differently in relation to one another. Forexample, internal angles ϑ_(i2), ϑ_(i6), and ϑ_(i7) of internal corners304B, 304F, and 304G, respectively, as well as external angle ϑ_(e3) ofexternal corner 306C, may each be substantially the same, for example afirst angle of about 140 degrees, as shown in FIG. 3. Furthermore,internal angles ϑ_(i1), ϑ_(i3), ϑ_(i4), ϑ_(i5), ϑ_(i8), and ϑ_(i9) ofinternal corners 304A, 304C, 304D, 304E, 304H, and 304I, respectively,as well as external angles ϑ_(e1) and ϑ_(e2) of external corners 306Aand 306B, respectively, may each substantially the same, for example asecond angle of about 110 degrees, as shown in FIG. 3. Thus, asdemonstrated in FIG. 3, three of the internal angles (e.g., ϑ_(i2),ϑ_(i6), and ϑ_(i7)) and one of the external angles (e.g., ϑ_(e3)) may besubstantially the same (e.g., a first angle measurement of about 140degrees); and the other six of the internal angles (e.g., ϑ_(i3),ϑ_(i4), ϑ_(i5), ϑ_(i8), and ϑ_(i9)) and the other two of the externalangles (e.g., ϑ_(e1) and ϑ_(e2)) may be substantially the same (e.g., asecond angle measurement of about 110 degrees). Moreover, it is furthercontemplated, but not shown, that three of the internal angles (e.g.,ϑ_(i2), ϑ_(i6), and ϑ_(i7)) and one of the external angles (e.g.,ϑ_(e3)) may be substantially the same, having a first angle measurementranging from about 30 to 170 degrees; that another three of the internalangles (e.g., ϑ_(i1), ϑ_(i5), and ϑ_(9i)) and another one of theexternal angles (e.g., ϑ_(e1)) may be substantially the same, having asecond angle measurement ranging from about 90 to 170 degrees; that yetanother three of the internal angles (e.g., ϑ_(i3), ϑ_(i4), and ϑ_(i8))and another one of the external angles (e.g., ϑ_(e2)) may besubstantially the same, having a third angle measurement ranging fromabout 90 to 170 degrees; and the first angle measurement, second anglemeasurement, and third angle measurement may each be substantiallydifferent from one another.

Rather than keeping all of the cross-sectional lengths L₁-L₁₂substantially the same, the cross-sectional lengths L₁-L₁₂ of each sideof the cells of a cellular structure in accordance with the presentdisclosure may be sized differently in relation to one another. Forexample, as demonstrated in exemplary embodiment of FIG. 3, each of thesides 302A, 302C, 302D, 302F, 302H, 302I, 302J and 302K has the samecross-sectional length L_(a) (i.e., L₁=L₃=L₄=L₆=L₈=L₉=L₁₀=L₁₁=L_(a)),and each of the sides 302B, 302E, 302G and 302L has the samecross-sectional length L_(b) (i.e., L₂=L₅=L₇=L₁₂=L_(b)), butcross-sectional length L_(a) and cross-sectional length L_(b) aresubstantially different, such that a ratio of the cross-sectional lengthL_(a) of sides 302A, 302C, 302D, 302F, 302H, 302I, 302J and 302K to thecross-sectional length L_(b) of sides 302B, 302E, 302G and 302L (i.e.,L_(a):L_(b) ratio) is about 1:2. The L_(a):L_(b) ratio of a crosssection of a cell of a cellular structure in accordance to the presentdisclosure may range from about 1:5 to about 5:1.

In another further exemplary embodiment, not shown, four of the sideshave the same first cross-sectional length L_(c) (i.e.,L₁=L₃=L₈=L₁₀=L_(a)), another four of the sides have the same secondcross-sectional length L_(d) (i.e., L₂=L₅=L₇=L₁₂=L_(d)), and yet anotherfour of the sides have the same third cross-sectional length L_(e)(i.e., L₄=L₆=L₉=L₁₁=L_(d)), but the first cross-sectional length L_(c),second cross-sectional length L_(d), and third cross-sectional lengthL_(e) are substantially different. In such an embodiment, a ratio of thefirst cross-sectional length L_(c) to the second cross-sectional lengthL_(d) may range from about 1:5 to about 5:1; a ratio of the secondcross-sectional length L_(d) to the third cross-sectional length L_(e)may range from about 1:5 to about 5:1; and a ratio of the firstcross-sectional length L_(c) to the third cross-sectional length L_(e)may range from about 1:5 to about 5:1. It is further contemplated thateach of the cross-sectional lengths L_(a), L_(b), L_(c), L_(d), andL_(e), as they are defined above, may be tuned to be a different sizeand still a plurality of the cells tuned in this manner is capable ofbeing interconnected such that there is no void between any of thetwelve cornered cells.

Turning to FIG. 4, an alternative exemplary embodiment of a structuralcomponent 400 is illustrated, which shows a detailed top view ofstructural component 400. The interior of structural component 400 isentirely filled with a cellular structure made up of interconnectedcells 300 with a twelve-cornered cross section or fragments thereof.Alternatively, although not shown, it is contemplated that the interiorof a structural component may be partially filled with a cellularstructure made up of interconnected cells 300 with a twelve-corneredcross section. The cellular structure 300 may extend along a full lengthof the structural component 400 or may extend only along a portion ofthe length of the structural component. Additionally or alternatively, aplurality of cellular structures 301 may be provided in the structuralcomponent 400, for example, stacked one on top of another to fill alength of the structural component 400. Additionally or alternatively,as previously discussed, a portion of one or more of the cellularstructures 301 may contain at least some type of filling to provideinsulation against sound and/or heat and/or to add additional strength.Further, although not shown, it is contemplated that the interior of astructural component may be only partially filled with a cellularstructure made up of interconnected cells 300 with a twelve-corneredcross section (e.g., at least a portion of one of a width, depth, orheight (length) of the structural component may not contact a portion ofone or more cellular structures contained within the structuralcomponent).

Each cell 300 of the cellular structure of the structural component 400has a twelve-cornered cross section with nine internal corners and threeexternal corners. The various internal angles ϑ_(i1)-ϑ_(i9) of eachinternal corner and the various external angles ϑ_(e1)-ϑ_(e3) of eachexternal corner are sized as set forth in the above description of FIG.3. Additionally, each side of the cells 300 has the same cross-sectionalthickness and the lengths are tuned with respect to one another asdescribed above. Tuning parameters of the twelve-cornered cross sectionof each cell in this manner allows a plurality of the cells to beinterconnected such that there is no void between any of the twelvecornered cells. In other words, all of the full-size cells (i.e., cellsthat are not cut off by a side or surface of the structural component)with a twelve-cornered cross section are interconnected together so thatthere are no gaps or alternative shaped cells therebetween. In this way,a cellular structure is provided that consists entirely ofinterconnected cells that each have a twelve-cornered cross section withnine internal corners and three external corners.

More generally, the various exemplary embodiments of the presentteachings contemplate, for example, structural components with interiorcellular structure having cells with cross-sectional sides havingvariable cross-sectional thicknesses, and/or having variable taperedlongitudinal walls and edges. Various additional exemplary embodimentscontemplate structural components with at least one side or surface thatis open or defined by at least one panel, wall, or other type of coverstructure, and that the one or more side or surface is bent and/orcurved. Moreover, to further adjust a structural components foldingpattern and/or peak load capacity, various additional exemplaryembodiments also contemplate structural components and/or the cells ofthe cellular structure thereof having trigger holes, flanges, and/orconvolutions as would be understood by those of ordinary skill in theart.

Additionally, structural components may incorporate multiple cellularstructures, with each cellular structure having cells with differentsized parameters and/or different materials in accordance with thepresent disclosure. Combinations of one or more of the above describedvariations are also contemplated. For example, a plurality of cellularstructure layers may be overlaid onto one another other, such that afirst cellular structure layer has differently sized cells, longitudinallength, and/or materials than that of a second cellular structure layer.Overlaid first and second cellular structure layers may optionally haveone or more plate layers disposed between them to facilitate bonding thecellular structure layers together, and/or to provide additionalstrength and stiffness.

As discussed and embodied herein, multiple tunable parameters—includingbut not limited to the lengths L₁-L₁₂ and thicknesses T₁-T₁₂ of thesides of the cells, the internal angles ϑ_(i1)-ϑ_(i8) and externalangles ϑ_(e1)-ϑ_(e4) of the corners, may all be tuned within the samecellular structure. These parameters all may be tuned within the samecellular structure to provide desired characteristics in the structuralcomponent.

In the illustrated embodiments of FIGS. 1-4, the cellular structureand/or the entire structural component may have a one-piececonstruction. As stated above, the one-piece constructions shown inFIGS. 1 through 4 are exemplary only and the present teachingscontemplate structural component and cellular structures thereof thathave other constructions such as two-piece construction or having threeor more pieces. For example, the cellular structure may be a separateconstruction from the one or more panel, wall, or other type of coverstructure that defines the one or more one side or surface of astructural component, thereby providing a structural component with aninterior cellular structure that is of at least a two-piececonstruction.

To demonstrate the improved strength and performance features of acellular structure consisting of cells having a twelve-cornered crosssection with nine internal angles and three external angles inaccordance with the present disclosure, the inventor compared variousexisting and conventional cellular cross section designs totwelve-cornered cellular cross sections based on the designs disclosedherein. Exemplary structural components with interior cellularstructures were modeled and compression simulation runs were conducted,as shown and described below with reference to FIGS. 5A-26.

Finite element models of structural components with interior cellularstructures having interconnected cells with varying shapes (i.e., crosssections) having the same thickness and longitudinal length weredeveloped as illustrated in FIGS. 5A-5C and 6A-6C. FIGS. 5A and 6A showtop and perspective views, respectively, of a structural component 500with an interior cellular structures having interconnected cells witheach full cell having a basic, four-cornered cross section (i.e., squareshape). FIGS. 5B and 6B show top and perspective views, respectively, ofa structural component 600 with an interior cellular structures havinginterconnected cells with each full cell having a basic, six-corneredcross section (i.e., regular hexagon shape). FIGS. 5C and 6C show topand perspective views, respectively, of a structural component 200 withan interior cellular structures having interconnected cells with eachfull cell having a twelve-cornered cross section, like that of FIGS.2A-2B as described above.

The structural components 200, 500, 600 were modeled to have as close tothe same total number of cells as possible. The cellular structure ofstructural component 500 has 49 square cells, the cellular structure ofstructural component 600 has 48 regular hexagon cells, and the cellularstructure of structural component 200 has 51 twelve-cornered cells.

The structural components 200, 500, 600 have the approximately the sametotal mass, mass per cell, side thicknesses, and longitudinal length(i.e., length along the z-axis). By virtue of maintaining the totalmass, per cell mass, side thicknesses, and total number of cellsapproximately the same, structural components 200, 500, 600 each havevaried lateral dimensions (i.e., lengths along the x- and y-axes). Inparticular, structural component 500 was modeled to have lateraldimensions of 183 mm×183 mm; structural component 600 was modeled tohave lateral dimensions of 190 mm×165 mm; and structural component 200was modeled to have lateral dimensions of 147 mm×154 mm. Thelongitudinal length of each structural component 200, 500, and 600 is100 mm.

To compare the structural components 200, 500, 600 with interiorcellular structures having interconnected cells with varying shapes,exemplary structural components 200, 500, 600 with interior cellularstructure were modeled twice as structurally described above. In thefirst modeling, the cellular structure of the structural components 200,500, 600 were made of aluminum. In the second modeling, the cellularstructure of the structural components 200, 500, 600 were made ofpolymer. Multiple finite element experimental test runs were conductedfor both the aluminum and polymer versions of structural components 200,500, and 600, as shown and described below with reference to FIGS. 7-14.FIGS. 7-10 relate to the experimental test runs that were conducted forthe aluminum versions. FIGS. 11-14 relate to the experimental test runsthat were conducted for the polymer versions.

The test runs for each structural component simulated an impact with thesame boundary condition, rigid mass (e.g. an impactor), impact speed,and initial kinetic energy.

FIGS. 7A-7C shows aluminum versions of modeled structural components500, 600, and 200, respectively, at a time interval of 8 millisecondsduring a simulated dynamic crush. During each dynamic crush, theimpactor is propelled by a gas gun with a designated mass and initialimpact velocity which creates a designated initial kinetic energy. Theinitial kinetic energy crushes the structural components and the initialkinetic energy is transferred into the internal energy of the structuralcomponents and cellular structures thereof. Performance of eachstructural component and cellular structure thereof can be compared bymeasuring the crush displacement, crush force, and specific energyabsorption of each structural component. As shown in FIGS. 7A-7C, duringthe simulated dynamic crush, the structural component 200 having analuminum cellular structure with twelve-cornered cells in accordancewith the present disclosure demonstrated shorter crush displacement andsmaller folding length than the structural components 500 and 600 havingan aluminum cellular structure with square and regular hexagon cells,respectively. Additionally, as shown in FIGS. 7A-7C, aluminum versionsof structural components 500 and 600 undesirably exhibited moreirregular crushing patterns, as evidenced, in particular, by theundesirable buckling and/or more severe plastic deformation in lowerportions of structural components 500 and 600.

FIG. 8 graphically portrays the dynamic crush force (in kN) absorbedaxially on the modeled aluminum version of exemplary structuralcomponents 200, 500 and 600, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIGS. 7A-7C. Thecrush force (in kN) values of the graph have been normalized to accountfor the slightly different number of cells and mass of each of thestructural components 200, 500 and 600, such that a normalizedcomparison can be made on a per cell and per unit mass basis. As shownin FIG. 8, the aluminum twelve-cornered cells of the cellular structureof the structural component 200 in accordance with the presentdisclosure could sustain a much higher crushing force for a givenresulting crushing distance as compared with the aluminum square andregular hexagon cells of the cellular structures of the structuralcomponents 500 and 600, respectively. Specifically, when averaged overthe range of 0 to 60 mm of displacement, the aluminum twelve-corneredcells of the cellular structure of the structural component 200accordance with the present disclosure achieved about a 50.77% increasein normalized average crush force as compared with the aluminum regularhexagon cells of the cellular structure of the structural component 600.The aluminum twelve-cornered cells of the cellular structure of thestructural component 200 also achieved about a 86.77% increase innormalized average crush force (over the range of 0 to 60 mmdisplacement) as compared with the aluminum square cells of the cellularstructure of the structural component 500.

FIG. 9 graphically portrays the dynamic axial crush energy (in kN-mm)absorbed axially by the modeled aluminum version of exemplary structuralcomponents 200, 500 and 600, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIGS. 7A-7C. Thecrush energy (in kN-mm) values of the graph have been normalized toaccount for the slightly different number of cells and mass of eachstructural components 200, 500 and 600, such that a comparison can bemade on a per cell and per unit mass basis. As shown in FIG. 9 thealuminum twelve-cornered cells of the cellular structure of thestructural component 200 in accordance with the present disclosure couldabsorb the same total kinetic energy of the impact over a much shorterdistance as compared the aluminum square and regular hexagon cells ofthe cellular structures of the structural components 500 and 600,respectively. Specifically, for example, at 60 mm displacement thealuminum twelve-cornered cells of the cellular structure of thestructural component 200 accordance with the present disclosure hadabsorbed about 50.77% more energy as compared to the amount of energyabsorbed by the aluminum regular hexagon cells of the cellular structureof the structural component 600 at a displacement of 60 mm. The aluminumtwelve-cornered cells of the cellular structure of the structuralcomponent 200 accordance with the present disclosure also had absorbedabout 86.77% more energy at 60 mm displacement as compared to the amountof energy absorbed by the aluminum square cells of the cellularstructure of the structural component 500 at a displacement of 60 mm.

A quasi-static crush of aluminum versions of modeled structuralcomponents 500, 600, and 200, respectively, was also simulated. Theresults of the simulated quasi-static crush for each aluminum model aregraphically portrayed in FIG. 10. During each quasi-static crush theimpact speed is slow (e.g., 1 in/min). An impactor compresses thestructural components with a controlled displacement. Therefore, allstructural components reach the same crush distance with the same crushtime. Thus, subjecting structural components with various cellularstructures to a quasi-static crush provides a comparison of theresistance to deformation (including the deformation severity in elasticrange and plastic range) and the peak force of the structuralcomponents. As used herein, the term “peak force” is defined as themaximum load of compressive force that a structure can withstand beforeexhibiting plastic deformation (as opposed to elastic deformation). Aperson of ordinary skill in the art will understand that plasticdeformation is permanent, non-reversible deformation that will remainafter removal of the compression load, and that elastic deformation istemporary, reversible deformation that will diminish upon removal of thecompression load. The quasi-static loading condition informs how astructure will respond in situations such as, for example, loading ofcargo and/or passengers.

In the simulated quasi-static crush of the aluminum versions of modeledstructural components 500, 600, and 200, the aluminum structuralcomponent 200 was observed to exhibit less deformation at each level ofcontrolled displacement, including in both the elastic and plasticdeformation ranges, as compared with the aluminum structural components500 and 600, respectively. Additionally, the observed deformation spreadto the lower portions of the cellular walls faster in structuralcomponents 500 and 600 than in structural component 200. Accordingly,the plastic deformation that occurred in the structural component 200was more localized, in that it was concentrated in regions close to theimpactor, while the plastic deformation of the structural components 500and 600 was more extensive, in that it spread to the entire structure.The results indicate that the structural component 200 has higherresistance to elastic and plastic deformation compared to the structuralcomponents 500 and 600. If plastic deformation does occur under a verysevere loading condition, a structural component 200 will exhibit lesssevere and more locally concentrated plastic deformation, and istherefore expected to be easier and less costly to repair.

FIG. 10 graphically portrays the normalized crush force (in kN) absorbedaxially on the modeled aluminum version of exemplary structuralcomponents 200, 500 and 600, and the associated axial crush displacement(in mm) for the simulated quasi-static crush described above. The crushforce (in kN) values of the graph have been normalized to account forthe slightly different number of cells and mass of each structuralcomponents 200, 500 and 600, such that a comparison can be made on a percell and per unit mass basis. As shown in FIG. 10, aluminumtwelve-cornered cells of the cellular structure of the structuralcomponent 200 accordance with the present disclosure demonstrated thehigher normalized peak force as compared with the aluminum square andregular hexagon cells of the cellular structures of the structuralcomponents 500 and 600, respectively. Specifically, the aluminumtwelve-cornered cells of the cellular structure of the structuralcomponent 200 accordance with the present disclosure achieved anormalized peak force of about 9.68 kN, the aluminum regular hexagoncells of the cellular structure of the structural component 600 had anormalized peak force of about 5.95 kN, and the aluminum square cells ofthe cellular structure of the structural component 500 had a normalizedpeak force of about 4.19 kN. Thus, the aluminum twelve-cornered cells ofthe cellular structure of the structural component 200 accordance withthe present disclosure achieved about a 62.7% increase in normalizedpeak force as compared with the aluminum regular hexagon cells of thecellular structure of the structural component 600 and about a 131.0%increase in normalized peak force as compared with the aluminum squarecells of the cellular structure of the structural component 500. Theabove results confirm that the structural component 200 can sustain muchhigher load before exhibiting plastic deformation than the structuralcomponents 500 and 600.

Turning now to the polymer versions, FIG. 11 shows polymer versions ofmodeled structural components 500, 600, and 200 at a time interval of 8milliseconds of a simulated dynamic crush, respectively. During eachdynamic crush, the impactor is propelled by a gas gun with a designatedmass and initial impact velocity which creates a designated initialkinetic energy. The initial kinetic energy crushes the structuralcomponents and the initial kinetic energy is transferred into theinternal energy of the structural components and cellular structuresthereof. Performance of each structural component and cellular structurethereof can be compared by measuring the crush displacement, crushforce, and specific energy absorption of each structural component. Asshown in FIG. 11, during the simulated dynamic crush, the structuralcomponent 200 having a polymer cellular structure with twelve-corneredcells in accordance with the present disclosure demonstrated shortercrush displacement than the structural components 500 and 600 having apolymer cellular structure with square and regular hexagon cells,respectively. Also, the twelve-cornered cells in the structuralcomponent 200 exhibited a smaller folding length than the square andregular hexagon cells in the structural components 500 and 600,respectively. Additionally, as shown in FIG. 11, polymer versions ofstructural components 500 and 600 undesirably exhibited more irregularcrushing patterns, as evidenced, in particular, by the undesirablebuckling and/or more severe plastic deformation in lower portions ofstructural components 500 and 600.

FIG. 12 graphically portrays the dynamic crush force (in kN) absorbedaxially on the modeled polymer version of exemplary structuralcomponents 200, 500 and 600, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 11. Thecrush force (in kN) values of the graph have been normalized to accountfor the slightly different number of cells and mass of each structuralcomponents 200, 500 and 600, such that a comparison can be made on a percell and per unit mass basis. As shown in FIG. 12, the polymertwelve-cornered cells of the cellular structure of the structuralcomponent 200 in accordance with the present disclosure could sustain amuch higher crushing force for a given resulting crushing distance ascompared with the polymer square and regular hexagon cells of thecellular structures of the structural components 500 and 600,respectively. Specifically, when averaged over the range of 0 to 60 mmof displacement, the polymer twelve-cornered cells of the cellularstructure of the structural component 200 accordance with the presentdisclosure achieved about a 27.71% increase in normalized average crushforce as compared with the polymer regular hexagon cells of the cellularstructure of the structural component 600. The polymer twelve-corneredcells of the cellular structure of the structural component 200 alsoachieved about a 57.85% increase in normalized average crush force (overthe range of 0 to 60 mm displacement) as compared with the polymersquare cells of the cellular structure of the structural component 500.

FIG. 13 graphically portrays the dynamic axial crush energy (in kN-mm)absorbed axially by the modeled polymer version of exemplary structuralcomponents 200, 500 and 600, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 11. Thecrush energy (in kN-mm) values of the graph have been normalized toaccount for the slightly different number of cells and mass of eachstructural components 200, 500 and 600, such that a comparison can bemade on a per cell and per unit mass basis. As shown in FIG. 13 thepolymer twelve-cornered cells of the cellular structure of thestructural component 200 in accordance with the present disclosure couldabsorb the same total kinetic energy of the impact over a much shorterdistance as compared the polymer square and regular hexagon cells of thecellular structures of the structural components 500 and 600,respectively. Specifically, for example, at 60 mm displacement thepolymer twelve-cornered cells of the cellular structure of thestructural component 200 accordance with the present disclosure hadabsorbed about 27.71% more energy as compared to the amount of energyabsorbed by the polymer regular hexagon cells of the cellular structureof the structural component 600 at a displacement of 60 mm. The polymertwelve-cornered cells of the cellular structure of the structuralcomponent 200 accordance with the present disclosure also had absorbedabout 57.85% more energy at 60 mm displacement as compared to the amountof energy absorbed by the polymer square cells of the cellular structureof the structural component 500 at a displacement of 60 mm.

A quasi-static crush of polymer versions of modeled structuralcomponents 500, 600, and 200, respectively, was also simulated. Theresults of the simulated quasi-static crush for each polymer model aregraphically portrayed in FIG. 14. During each quasi-static crush theimpact speed is slow (e.g., 1 in/min). An impactor compresses thestructural components with a controlled displacement. Therefore, allstructural components reach the same crush distance with the same crushtime. Thus, subjecting structural components with various cellularstructures to a quasi-static crush provides a comparison of theresistance to plastic deformation including, the deformation severity inelastic and plastic ranges, and the peak force of the structuralcomponents.

In the simulated quasi-static crush of the polymer versions of modeledstructural components 500, 600, and 200, the polymer structuralcomponent 200 was observed to exhibit less deformation at each level ofcontrolled displacement, including in both the elastic and plasticdeformation ranges, as compared with the polymer structural components500 and 600, respectively. Additionally, the observed deformation spreadto the lower portions of the cellular walls faster in structuralcomponents 500 and 600 than in structural component 200. Accordingly,the plastic deformation that occurred in the structural component 200was more localized, in that it was concentrated in regions close to theimpactor, while the plastic deformation of the structural components 500and 600 was more extensive, in that it spread to the entire structure.The results indicate that the structural component 200 has higherresistance to elastic and plastic deformation compared to the structuralcomponents 500 and 600. If plastic deformation does occur under a verysevere loading condition, a structural component 200 will exhibit lesssevere and more locally concentrated plastic deformation, and istherefore expected to be easier and less costly to repair.

FIG. 14 graphically portrays the normalized crush force (in kN) absorbedaxially on the modeled polymer version of exemplary structuralcomponents 200, 500 and 600, and the associated axial crush displacement(in mm) for the simulated quasi-static crush described above. The crushforce (in kN) values of the graph have been normalized to account forthe slightly different number of cells and mass of each structuralcomponents 200, 500 and 600, such that a comparison can be made on a percell and per unit mass basis. As shown in FIG. 14, polymertwelve-cornered cells of the cellular structure of the structuralcomponent 200 accordance with the present disclosure demonstrated thehigher normalized peak force as compared with the polymer square andregular hexagon cells of the cellular structures of the structuralcomponents 500 and 600, respectively. Specifically, the polymertwelve-cornered cells of the cellular structure of the structuralcomponent 200 accordance with the present disclosure achieved anormalized peak force of about 6.72 kN, the polymer regular hexagoncells of the cellular structure of the structural component 600 had anormalized peak force of about 5.44 kN, and the polymer square cells ofthe cellular structure of the structural component 500 had a normalizedpeak force of about 4.37 kN. Thus, the polymer twelve-cornered cells ofthe cellular structure of the structural component 200 accordance withthe present disclosure achieved about a 23.5% increase in normalizedpeak force as compared with the polymer regular hexagon cells of thecellular structure of the structural component 600 and about a 53.8%increase in normalized peak force as compared with the polymer squarecells of the cellular structure of the structural component 500. Theabove results confirm that the structural component 200 can sustain muchhigher load before exhibiting plastic deformation than the structuralcomponents 500 and 600.

For further comparison, finite element models of structural componentswith interior cellular structures having interconnected cells withvarying shapes (i.e., cross sections) having the same thickness weredeveloped as illustrated in FIG. 15A. FIG. 15A shows perspective viewsof a structural component 500 with an interior cellular structureshaving interconnected cells with each full cell having a basic,four-cornered cross section (i.e., square shape) (like that of FIGS. 5Aand 6A as described above), another structural component 700 with aninterior cellular structures having interconnected cells with each fullcell having a basic, four-cornered cross section (i.e., square shape),and a structural component 200 with an interior cellular structureshaving interconnected cells with each full cell having a twelve-corneredcross section (like that of FIGS. 2A-2B as described above).

The structural components 200, 500, 700 were modeled to have as close tothe same total number of cells as possible. The cellular structure ofstructural component 500 has 49 square cells, the cellular structure ofstructural component 700 has 49 square cells, and the cellular structureof structural component 200 has 51 twelve-cornered cells.

The structural components 200 and 500 have the approximately the sametotal mass, mass per cell, side thicknesses, and longitudinal length(i.e., length along the z-axis). By virtue of maintaining the totalmass, per cell mass, side thicknesses, and total number of cellsapproximately the same, structural components 200 and 500 each havevaried lateral dimensions (i.e., lengths along the x- and y-axes). Inparticular, structural component 500 was modeled to have lateraldimensions of 183 mm×183 mm; and structural component 200 was modeled tohave lateral dimensions of 147 mm×154 mm. To provide further comparison,structural component 700 was modeled to have approximately the same sidethickness and longitudinal length, but an increased total mass, and massper cell. Accordingly, structural component 700 has varied lateraldimensions. In particular, structural component 700 as modeled to havelateral dimensions of 341 mm×341 mm. The longitudinal length of eachstructural component 200, 500, and 700 is 100 mm.

To compare the structural components 200, 500, 700 with interiorcellular structures having interconnected cells with varying shapes,exemplary structural components 200, 500, 700 with interior cellularstructure were modeled twice as structurally described above. In thefirst modeling, the cellular structure of the structural components 200,500, 700 were made of aluminum. In the second modeling, the cellularstructure of the structural components 200, 500, 700 were made ofpolymer. Multiple finite element experimental test runs were conductedfor both the aluminum and polymer versions of structural components 200,500, and 700, as shown and described below with reference to FIGS.15A-20. FIGS. 15A-17 relate to the experimental test runs that wereconducted for the aluminum versions. Notably, the aluminum version ofcellular structure 700 shown in FIG. 15A was modeled to have about 86%more mass than the aluminum versions of cellular structures 500 and 200.FIGS. 18A-20 relate to the experimental test runs that were conductedfor the polymer versions. Notably, the polymer version of cellularstructure 700 shown in FIG. 15A was modeled to have about 57% more massthan the polymer versions of cellular structures 500 and 200.

The test runs for each structural component simulated an impact with thesame boundary condition, rigid mass (e.g. an impactor), impact speed,and initial kinetic energy.

FIG. 15B shows aluminum versions of modeled structural components 500,700, and 200 at a time interval of 8 milliseconds of a simulated dynamiccrush. During each dynamic crush, the impactor is propelled by a gas gunwith a designated mass and initial impact velocity which creates adesignated initial kinetic energy. The initial kinetic energy crushesthe structural components and the initial kinetic energy is transferredinto the internal energy of the structural components and cellularstructures thereof. Performance of each structural component andcellular structure thereof can be compared by measuring the crushdisplacement, crush force, and specific energy absorption of eachstructural component. As shown in FIG. 15B, throughout the simulateddynamic crush, the structural component 200 having an aluminum cellularstructure with twelve-cornered cells in accordance with the presentdisclosure demonstrated shorter crush displacement than the structuralcomponents 500 and 700 having an aluminum cellular structure with squarecells. Also, the twelve-cornered cells in the structural component 200exhibited smaller folding lengths than the square and regular hexagoncells in the structural components 500 and 700, respectively.Additionally, as shown in FIG. 15B, aluminum versions of structuralcomponents 500 and 700 undesirably exhibited more irregular crushingpatterns, as evidenced, in particular, by the undesirable bucklingand/or more severe plastic deformation in lower portions of structuralcomponents 500 and 700.

FIG. 16 graphically portrays the dynamic crush force (in kN) absorbedaxially on the modeled aluminum version of exemplary structuralcomponents 200, 500 and 700, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 15B. Asshown in FIG. 16, the aluminum twelve-cornered cells of the cellularstructure of the structural component 200 in accordance with the presentdisclosure could sustain a higher crushing force for a given resultingcrushing distance as compared with the aluminum square cells of thecellular structures of the structural components 500 and 700.Specifically, when averaged over the range of 0 to 60 mm ofdisplacement, the twelve-corner-celled aluminum cellular structure ofthe structural component 200 accordance with the present disclosureachieved about a 94.7% increase in average crush force as compared withthe square-celled aluminum cellular structure of the structuralcomponent 500. The twelve-corner-celled aluminum cellular structure ofthe structural component 200 also achieved about a 22.9% increase inaverage crush force (over the range of 0 to 60 mm displacement) ascompared with the square-celled aluminum cellular structure of thestructural component 700 despite the fact that structural component 700has a much larger total mass as well as larger lateral dimensions thanstructural component 200. Additionally, an approximation of a simulateddynamic loading condition of an aluminum structural component 200 mhaving a cellular structure with 45 total twelve-cornered cells and 88%of the mass of the aluminum cellular structure 200 was made byextrapolation of the data for the structural component 200 (which has 51total cells). With about 88% of mass of structural component 200, theapproximated simulation results show that structural component 200 mstill achieved about a 72% increase in average crush force (over therange of 0 to 60 mm displacement) as compared with the square-celledaluminum cellular structure of the structural component 500 at adisplacement of 60 mm, even though structural component 500 has a largertotal mass, more cells, and larger lateral dimensions than thestructural component 200 m. The twelve-corner-celled aluminum cellularstructure of the structural component 200 m also achieved about a 8%increase in average crush force (over the range of 0 to 60 mmdisplacement) as compared to the amount of energy absorbed by thesquare-celled aluminum cellular structure of the structural component700 despite the fact that structural component 700 has a much largertotal mass, more cells, and much larger lateral dimensions than thestructural component 200 m.

FIG. 17 graphically portrays the dynamic axial crush energy (in kN-mm)absorbed axially by the modeled aluminum version of exemplary structuralcomponents 200, 500 and 700, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 15B. Asshown in FIG. 17, the aluminum twelve-cornered cells of the cellularstructure of the structural component 200 in accordance with the presentdisclosure could absorb the same total kinetic energy of the impact overa shorter distance as compared the aluminum square cells of the cellularstructures of the structural components 500 and 700. Specifically, forexample, at 60 mm displacement the twelve-corner-celled aluminumcellular structure of the structural component 200 accordance with thepresent disclosure had absorbed about 94.7% more energy as compared tothe amount of energy absorbed by the square-celled aluminum cellularstructure of the structural component 500 at a displacement of 60 mm.The twelve-corner-celled aluminum cellular structure of the structuralcomponent 200 accordance with the present disclosure also had absorbedabout 22.9% more energy at 60 mm displacement as compared to the amountof energy absorbed by square-celled aluminum cellular structure of thestructural component 700 at a displacement of 60 mm despite the factthat structural component 700 has a much larger total mass as well aslarger lateral dimensions than structural component 200. Additionally,an approximation of a simulated dynamic loading condition of an aluminumstructural component 200 m having a cellular structure with 45 totaltwelve-cornered cells and 88% of the mass of the aluminum cellularstructure 200 was made by extrapolation of the data for the structuralcomponent 200 (which has 51 total cells). With about 88% of mass ofstructural component 200, the approximated simulation results show thatstructural component 200 m still absorbed about 72% more energy at 60 mmdisplacement as compared to the amount of energy absorbed by thesquare-celled aluminum cellular structure of the structural component500 at a displacement of 60 mm, even though structural component 500 hasa larger total mass, more cells, and larger lateral dimensions than thestructural component 200 m. The twelve-corner-celled aluminum cellularstructure of the structural component 200 m also absorbed about 8% moreenergy at 60 mm displacement as compared to the amount of energyabsorbed by the square-celled aluminum cellular structure of thestructural component 700 despite the fact that structural component 700has a much larger total mass, more cells, and much larger lateraldimensions than the structural component 200 m.

Turning now to the polymer versions, FIGS. 18A and 18B show polymerversions of modeled structural components 500, 700, and 200 at timeintervals of 0 milliseconds and 8 milliseconds of a simulated dynamiccrush, respectively. During each dynamic crush, the impactor ispropelled by a gas gun with a designated mass and initial impactvelocity which creates a designated initial kinetic energy. The initialkinetic energy crushes the structural components and the initial kineticenergy is transferred into the internal energy of the structuralcomponents and cellular structures thereof. Performance of eachstructural component and cellular structure thereof can be compared bymeasuring the crush displacement, crush force, and specific energyabsorption of each structural component. As shown in FIG. 18B, duringthe simulated dynamic crush, the structural component 200 having apolymer cellular structure with twelve-cornered cells in accordance withthe present disclosure demonstrated shorter crush displacement than thestructural components 500 and 700 having a polymer cellular structurewith square cells, respectively. Also, the twelve-cornered cells in thestructural component 200 also exhibited smaller folding lengths than thesquare and regular hexagon cells in the structural components 500 and700, respectively. Additionally, as shown in FIG. 18B, polymer versionsof structural components 500 and 700 undesirably exhibited moreirregular crushing patterns, as evidenced, in particular, by theundesirable buckling and/or more severe plastic deformation in lowerportions of structural components 500 and 700.

FIG. 19 graphically portrays the dynamic crush force (in kN) absorbedaxially on the modeled polymer version of exemplary structuralcomponents 200, 500 and 700, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 18B. Asshown in FIG. 19, the polymer twelve-cornered cells of the cellularstructure of the structural component 200 in accordance with the presentdisclosure could sustain a higher crushing force for a given resultingcrushing distance as compared with the polymer square cells of thecellular structures of the structural components 500 and 700.Specifically, when averaged over the range of 0 to 60 mm ofdisplacement, the twelve-corner-celled polymer cellular structure of thestructural component 200 accordance with the present disclosure achievedabout a 68.8% increase in average crush force as compared with thesquare-celled polymer cellular structure of the structural component500. The twelve-corner-celled polymer cellular structure of thestructural component 200 also achieved about a 31.3% increase in averagecrush force (over the range of 0 to 60 mm displacement) as compared withthe square-celled polymer cellular structure of the structural component700 despite the fact that structural component 700 has a much largertotal mass as well as larger lateral dimensions than structuralcomponent 200. Additionally, an approximation of a simulated dynamicloading condition of an polymer structural component 200 m having acellular structure with 45 total twelve-cornered cells and 88% of themass of the aluminum cellular structure 200 was made by extrapolation ofthe data for the structural component 200 (which has 51 total cells).With about 88% of mass of structural component 200, the approximatedsimulation results show that structural component 200 m still achievedabout a 48% increase in average crush force (over the range of 0 to 60mm displacement) as compared with the square-celled polymer cellularstructure of the structural component 500 at a displacement of 60 mm,even though structural component 500 has a larger total mass, morecells, and larger lateral dimensions than the structural component 200m. The twelve-corner-celled polymer cellular structure of the structuralcomponent 200 m also achieved about a 15% increase in average crushforce (over the range of 0 to 60 mm displacement) as compared to theamount of energy absorbed by the square-celled polymer cellularstructure of the structural component 700 despite the fact thatstructural component 700 has a much larger total mass, more cells, andmuch larger lateral dimensions than the structural component 200 m.

FIG. 20 graphically portrays the dynamic axial crush energy (in kN-mm)absorbed axially by the modeled polymer version of exemplary structuralcomponents 200, 500 and 700, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 18B. Asshown in FIG. 20, the polymer twelve-cornered cells of the cellularstructure of the structural component 200 in accordance with the presentdisclosure could absorb the same total kinetic energy of the impact overa shorter distance as compared the polymer square cells of the cellularstructures of the structural components 500 and 700. Specifically, forexample, at 60 mm displacement the twelve-corner-celled polymer cellularstructure of the structural component 200 accordance with the presentdisclosure had absorbed about 68.8% more energy as compared to theamount of energy absorbed by the square-celled polymer cellularstructure of the structural component 500 at a displacement of 60 mm.The twelve-corner-celled polymer cellular structure of the structuralcomponent 200 accordance with the present disclosure also had absorbedabout 31.3% more energy at 60 mm displacement as compared to the amountof energy absorbed by square-celled polymer cellular structure of thestructural component 700 at a displacement of 60 mm despite the factthat structural component 700 has a much larger total mass as well aslarger lateral dimensions than structural component 200. Additionally,an approximation of a simulated dynamic loading condition of an polymerstructural component 200 m having a cellular structure with 45 totaltwelve-cornered cells and 88% of the mass of the polymer cellularstructure 200 was made by extrapolation of the data for the structuralcomponent 200 (which has 51 total cells). With about 88% of mass ofstructural component 200, the approximated simulation results show thatstructural component 200 m still absorbed about 48% more energy at 60 mmdisplacement as compared to the amount of energy absorbed by thesquare-celled polymer cellular structure of the structural component 500at a displacement of 60 mm, even though structural component 500 has alarger total mass, more cells, and larger lateral dimensions than thestructural component 200 m. The twelve-corner-celled polymer cellularstructure of the structural component 200 m also absorbed about 15% moreenergy at 60 mm displacement as compared to the amount of energyabsorbed by the square-celled polymer cellular structure of thestructural component 700 despite the fact that structural component 700has a much larger total mass, more cells, and much larger lateraldimensions than the structural component 200 m.

Additionally, for further comparison, finite element models ofstructural components with interior cellular structures havinginterconnected cells with varying shapes (i.e., cross sections) havingthe same thickness were developed as illustrated in FIG. 21A. FIG. 21Ashows perspective views of a structural component 600 with an interiorcellular structures having interconnected cells with each full cellhaving a basic, six-cornered cross section (i.e., regular hexagon shape)(like that of FIGS. 5B and 6B as described above), another structuralcomponent 800 with an interior cellular structures having interconnectedcells with each full cell having a basic, six-cornered cross section(i.e., regular hexagon shape), and a structural component 200 with aninterior cellular structures having interconnected cells with each fullcell having a twelve-cornered cross section (like that of FIGS. 2A-2B asdescribed above).

The structural components 200, 600, 800 were modeled to have as close tothe same total number of cells as possible. The cellular structure ofstructural component 600 has 48 hexagon cells, the cellular structure ofstructural component 800 has 48 regular hexagon cells, and the cellularstructure of structural component 200 has 51 twelve-cornered cells.

The structural components 200 and 600 have the approximately the sametotal mass, mass per cell, side thicknesses, and longitudinal length(i.e., length along the z-axis). By virtue of maintaining the totalmass, per cell mass, side thicknesses, and total number of cellsapproximately the same, structural components 200 and 600 each havevaried lateral dimensions (i.e., lengths along the x- and y-axes). Inparticular, structural component 600 was modeled to have lateraldimensions of 190 mm×165 mm; and structural component 200 was modeled tohave lateral dimensions of 147 mm×154 mm. To provide further comparison,structural component 800 was modeled to have approximately the same sidethickness and longitudinal length, but an increased total mass and massper cell, and longitudinal length. Accordingly, structural component 800has varied lateral dimensions. In particular, structural component 800as modeled to have lateral dimensions of 285 mm×248 mm. The longitudinallength of each structural component 200, 600, and 800 is 100 mm.

To compare the structural components 200, 600, 800 with interiorcellular structures having interconnected cells with varying shapes,exemplary structural components 200, 600, 800 with interior cellularstructure were modeled twice as structurally described above. In thefirst modeling, the cellular structure of the structural components 200,600, 800 were made of aluminum. In the second modeling, the cellularstructure of the structural components 200, 600, 800 were made ofpolymer. Multiple finite element experimental test runs were conductedfor both the aluminum and polymer versions of structural components 200,600, and 800, as shown and described below with reference to FIGS.21A-26. FIGS. 21A-23 relate to the experimental test runs that wereconducted for the aluminum versions. Notably, the aluminum version ofcellular structure 800 shown in FIG. 21A was modeled to have about 50%more mass than the aluminum versions of cellular structures 600 and 200.FIGS. 24A-26 relate to the experimental test runs that were conductedfor the polymer versions. Notably, the polymer version of cellularstructure 800 shown in FIG. 24A was modeled to have about 27% more massthan the polymer versions of cellular structures 600 and 200.

The test runs for each structural component simulated an impact with thesame boundary condition, rigid mass (e.g. an impactor), impact speed,and initial kinetic energy.

FIGS. 21A and 21B show aluminum versions of modeled structuralcomponents 600, 800, and 200 at time intervals of 0 and 8 millisecondsof a simulated dynamic crush, respectively. During each dynamic crush,the impactor is propelled by a gas gun with a designated mass andinitial impact velocity which creates a designated initial kineticenergy. The initial kinetic energy crushes the structural components andthe initial kinetic energy is transferred into the internal energy ofthe structural components and cellular structures thereof. Performanceof each structural component and cellular structure thereof can becompared by measuring the crush displacement, crush force, and specificenergy absorption of each structural component. As shown in FIG. 21B,throughout the simulated dynamic crush, the structural component 200having an aluminum cellular structure with twelve-cornered cells inaccordance with the present disclosure demonstrated shorter crushdisplacement than the structural components 600 and 800 having analuminum cellular structure with hexagonal cells. Also, thetwelve-cornered cells in the structural component 200 exhibited smallerfolding lengths than the square and regular hexagon cells in thestructural components 600 and 800 respectively. Additionally, as shownin FIG. 21B, aluminum versions of structural components 600 and 800undesirably exhibited more irregular crushing patterns, as evidenced, inparticular, by the undesirable buckling and/or more severe deformationin lower portions of structural components 600 and 800.

FIG. 22 graphically portrays the dynamic crush force (in kN) absorbedaxially on the modeled aluminum version of exemplary structuralcomponents 200, 600 and 800, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 21B. Asshown in FIG. 22, the aluminum twelve-cornered cells of the cellularstructure of the structural component 200 in accordance with the presentdisclosure could sustain a higher crushing force for a given resultingcrushing distance as compared with the aluminum regular hexagon cells ofthe cellular structures of the structural components 600 and 800.Specifically, when averaged over the range of 0 to 60 mm ofdisplacement, the twelve-corner-celled aluminum cellular structure ofthe structural component 200 accordance with the present disclosureachieved about a 59.6% increase in average crush force as compared withthe hexagon-celled aluminum cellular structure of the structuralcomponent 600. The twelve-corner-celled aluminum cellular structure ofthe structural component 200 also achieved about a 28.1% increase inaverage crush force (over the range of 0 to 60 mm displacement) ascompared with the hexagon-celled aluminum cellular structure of thestructural component 800 despite the fact that structural component 800has a much larger total mass as well as larger lateral dimensions thanstructural component 200. Additionally, an approximation of a simulateddynamic loading condition of an aluminum structural component 200 mhaving a cellular structure with 45 total twelve-cornered cells and 88%of the mass of the aluminum cellular structure 200 was made byextrapolation of the data for the structural component 200 (which has 51total cells). With about 88% of mass of structural component 200, theapproximated simulation results show that structural component 200 mstill achieved about a 41% increase in average crush force (over therange of 0 to 60 mm displacement) as compared with the hexagon-celledaluminum cellular structure of the structural component 500 at adisplacement of 60 mm, even though structural component 500 has a largertotal mass, more cells, and larger lateral dimensions than thestructural component 200 m. The twelve-corner-celled aluminum cellularstructure of the structural component 200 m also achieved about a 13%increase in average crush force (over the range of 0 to 60 mmdisplacement) as compared to the amount of energy absorbed by thehexagon-celled aluminum cellular structure of the structural component700 despite the fact that structural component 700 has a much largertotal mass, more cells, and much larger lateral dimensions than thestructural component 200 m.

FIG. 23 graphically portrays the dynamic axial crush energy (in kN-mm)absorbed axially by the modeled aluminum version of exemplary structuralcomponents 200, 600 and 800, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 21B. Asshown in FIG. 23, the aluminum twelve-cornered cells of the cellularstructure of the structural component 200 in accordance with the presentdisclosure could absorb the same total kinetic energy of the impact overa shorter distance as compared the aluminum regular hexagon cells of thecellular structures of the structural components 600 and 800.Specifically, for example, at 60 mm displacement thetwelve-corner-celled aluminum cellular structure of the structuralcomponent 200 accordance with the present disclosure had absorbed about59.6% more energy as compared to the amount of energy absorbed by thehexagon-celled aluminum cellular structure of the structural component600 at a displacement of 60 mm. The twelve-corner-celled aluminumcellular structure of the structural component 200 accordance with thepresent disclosure also had absorbed about 28.1% more energy at 60 mmdisplacement as compared to the amount of energy absorbed byhexagon-celled aluminum cellular structure of the structural component800 at a displacement of 60 mm despite the fact that structuralcomponent 800 has a much larger total mass as well as larger lateraldimensions than structural component 200. Additionally, an approximationof a simulated dynamic loading condition of an aluminum structuralcomponent 200 m having a cellular structure with 45 totaltwelve-cornered cells and 88% of the mass of the aluminum cellularstructure 200 was made by extrapolation of the data for the structuralcomponent 200 (which has 51 total cells). With about 88% of mass ofstructural component 200, the approximated simulation results show thatstructural component 200 m still absorbed about 41% more energy at 60 mmdisplacement as compared to the amount of energy absorbed by thehexagon-celled aluminum cellular structure of the structural component500 at a displacement of 60 mm, even though structural component 500 hasa larger total mass, more cells, and larger lateral dimensions than thestructural component 200 m. The twelve-corner-celled aluminum cellularstructure of the structural component 200 m also absorbed about 13% moreenergy at 60 mm displacement as compared to the amount of energyabsorbed by the hexagon-celled aluminum cellular structure of thestructural component 700 despite the fact that structural component 700has a much larger total mass, more cells, and much larger lateraldimensions than the structural component 200 m.

Turning now to the polymer versions, FIGS. 24A and 24B show polymerversions of modeled structural components 600, 800, and 200 at timeintervals of 0 and 8 milliseconds of a simulated dynamic crush,respectively. During each dynamic crush, the impactor is propelled by agas gun with a designated mass and initial impact velocity which createsa designated initial kinetic energy. The initial kinetic energy crushesthe structural components and the initial kinetic energy is transferredinto the internal energy of the structural components and cellularstructures thereof. Performance of each structural component andcellular structure thereof can be compared by measuring the crushdisplacement, crush force, and specific energy absorption of eachstructural component. As shown in FIG. 24B, during the simulated dynamiccrush, the structural component 200 having a polymer cellular structurewith twelve-cornered cells in accordance with the present disclosuredemonstrated shorter crush displacement than the structural components600 and 800 having a polymer cellular structure with regular hexagoncells. Also, the twelve-cornered cells in the structural component 200exhibited smaller folding lengths than the square and regular hexagoncells in the structural components 600 and 800, respectively.Additionally, as shown in FIG. 24B polymer versions of structuralcomponents 600 and 800 undesirably exhibited more irregular crushingpatterns, as evidenced, in particular, by the undesirable bucklingand/or more wide-spread deformation in lower portions of structuralcomponents 600 and 800.

FIG. 25 graphically portrays the dynamic crush force (in kN) absorbedaxially on the modeled polymer version of exemplary structuralcomponents 200, 600 and 800, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 24B. Asshown in FIG. 25, the polymer twelve-cornered cells of the cellularstructure of the structural component 200 in accordance with the presentdisclosure could sustain a higher crushing force for a given resultingcrushing distance as compared with the polymer hexagon cells of thecellular structures of the structural components 600 and 800.Specifically, when averaged over the range of 0 to 60 mm ofdisplacement, the twelve-corner-celled polymer cellular structure of thestructural component 200 accordance with the present disclosure achievedabout a 35.7% increase in average crush force as compared with thehexagon-celled polymer cellular structure of the structural component600. The twelve-corner-celled polymer cellular structure of thestructural component 200 also achieved about a 20.6% increase in averagecrush force (over the range of 0 to 60 mm displacement) as compared withthe hexagon-celled polymer cellular structure of the structuralcomponent 800 despite the fact that structural component 800 has a muchlarger total mass as well as larger lateral dimensions than structuralcomponent 200. Additionally, an approximation of a simulated dynamicloading condition of an aluminum structural component 200 m having acellular structure with 45 total twelve-cornered cells and 88% of themass of the polymer cellular structure 200 was made by extrapolation ofthe data for the structural component 200 (which has 51 total cells).With about 88% of mass of structural component 200, the approximatedsimulation results show that structural component 200 m still achievedabout a 19% increase in average crush force (over the range of 0 to 60mm displacement) as compared with the hexagon-celled polymer cellularstructure of the structural component 500 at a displacement of 60 mm,even though structural component 500 has a larger total mass, morecells, and larger lateral dimensions than the structural component 200m. The twelve-corner-celled polymer cellular structure of the structuralcomponent 200 m also achieved about a 6% increase in average crush force(over the range of 0 to 60 mm displacement) as compared to the amount ofenergy absorbed by the hexagon-celled polymer cellular structure of thestructural component 700 despite the fact that structural component 700has a much larger total mass, more cells, and much larger lateraldimensions than the structural component 200 m.

FIG. 26 graphically portrays the dynamic axial crush energy (in kN-mm)absorbed axially by the modeled polymer version of exemplary structuralcomponents 200, 600 and 800, and the associated axial crush displacement(in mm) for the simulated dynamic crush illustrated in FIG. 24B. Asshown in FIG. 26, the polymer twelve-cornered cells of the cellularstructure of the structural component 200 in accordance with the presentdisclosure could absorb the same total kinetic energy of the impact overa shorter distance as compared the polymer hexagon cells of the cellularstructures of the structural components 600 and 800. Specifically, forexample, at 60 mm displacement the twelve-corner-celled polymer cellularstructure of the structural component 200 accordance with the presentdisclosure had absorbed about 35.7% more energy as compared to theamount of energy absorbed by the hexagon-celled polymer cellularstructure of the structural component 500 at a displacement of 60 mm.The twelve-corner-celled polymer cellular structure of the structuralcomponent 200 accordance with the present disclosure also had absorbedabout 20.6% more energy at 60 mm displacement as compared to the amountof energy absorbed by hexagon-celled polymer cellular structure of thestructural component 800 at a displacement of 60 mm despite the factthat structural component 800 has a much larger total mass as well aslarger lateral dimensions than structural component 200. Additionally,an approximation of a simulated dynamic loading condition of an polymerstructural component 200 m having a cellular structure with 45 totaltwelve-cornered cells and 88% of the mass of the polymer cellularstructure 200 was made by extrapolation of the data for the structuralcomponent 200 (which has 51 total cells). With about 88% of mass ofstructural component 200, the approximated simulation results show thatstructural component 200 m still absorbed about 19% more energy at 60 mmdisplacement as compared to the amount of energy absorbed by thehexagon-celled polymer cellular structure of the structural component500 at a displacement of 60 mm, even though structural component 500 hasa larger total mass, more cells, and larger lateral dimensions than thestructural component 200 m. The twelve-corner-celled polymer cellularstructure of the structural component 200 m also absorbed about 6% moreenergy at 60 mm displacement as compared to the amount of energyabsorbed by the hexagon-celled polymer cellular structure of thestructural component 700 despite the fact that structural component 700has a much larger total mass, more cells, and much larger lateraldimensions than the structural component 200 m.

Cellular structures having interconnect cells with a twelve-corneredcross section in accordance with the present teachings may, therefore,allow improved impact and compression energy management over, forexample, cellular structures with basic polygonal cellular crosssections, including basic four-cornered and six-cornered polygonalcellular cross sections, while minimizing mass per unit length, providesmass saving solutions that reduce vehicle weight and meet new CorporateAverage Fuel Economy (CAFE) and emission standards.

Beyond the increased load carrying and energy absorption capabilities,structural components and cellular structures thereof in accordance withthe present teachings may provide additional advantages or benefits suchas increased bending energy absorption capacity, improved manufacturingfeasibility, reduced elastic and plastic deformation, higher plasticdeformation threshold, more locally concentrated plastic deformation,and better fitting of the shape amongst the other components of thecomplete structure (e.g., vehicle, as noted above).

In addition, a structural component having a cellular structure withinterconnected cells having a twelve-cornered cross section inaccordance with the present disclosure also may be tuned to accommodateunique packaging requirements for use in various structures.Incorporation of the cellular structures of the present disclosurewithin a structural component can also allow for use of a structuralcomponent having a peripheral cross section with a basic polygonalshape, such as a circular, oval, triangle, square, or rectangle. Byvirtue of the particular shape of the peripheral cross section of atleast some of the structural components, it may be easier to couple,bond, attach, or otherwise affix other device components to a structuralcomponent having a basic polygonal peripheral cross section and aninterior cellular structure having cells with a twelve-cornered crosssection in accordance with the present disclosure. Where the structureis a vehicle other structural components can include, but are notlimited to, strengthening ribs for casting or molding components, engineand gear box oil pans, transmission cases, intake manifolds, cylinderblocks, strut mounts, engine mounts or transmission mounts.

Structural components and/or cellular structures thereof in accordancewith the present teachings are contemplated for use as structuralmembers in a number of environments. For example, in a motor vehicle,(e.g., car, truck, van, ATV, RV, motorcycle, etc.), a structuralcomponent and/or cellular structure as disclosed herein is, or is atleast a part of, structural member that is a crush can, a bumper, afront horn, a front rail, a front side rail, a rear side rail, a rearrail, a frame cross member, a shotgun, a hinge-pillar, an A-pillar, aB-pillar, a C-pillar, a door beam, a cross car beam, a front header, arear header, a cow top, a roof rail, a lateral roof bow, a longitudinalroof bow, a body cross member, a back panel cross member, a rocker, anunderbody cross member, an engine compartment cross member, a roofpanel, a door, a floor, a deck lid, a lift gate, a hood, a rocker, atrim backing stiffener, a battery protective housing, a furniture item,and a body shell. In addition, the present disclosures can be applied toboth body-on-frame and unitized vehicles, or other types of structures.

FIGS. 27 and 28 show an exemplary vehicle frame and an exemplary vehicleupper body, respectively, which have structural members for whichstructural components having interior cellular structures, or a cellularstructure alone, with cells having a twelve-cornered cross section inaccordance with the present disclosure, can be used. FIG. 27 illustratesan exemplary embodiment of a vehicle frame 2700 with several componentsfor which or in which the cellular structures can be used. For example,the cellular structures in accordance with the present disclosure mayform or be used as a part of a front horn 2702, a front rail 2704, afront side rail 2706, a rear side rail 2708, a rear rail 2710, and/or asone or more cross members 2712. Likewise, FIG. 28 illustrates anexemplary embodiment of a vehicle upper body 2800 with severalcomponents for which or in which the cellular structures can be used.For example, the cellular structures in accordance with the presentdisclosure may be formed or be used as a part of a shotgun 2802, ahinge-pillar 2804, an A-pillar 2806, a B-pillar 2808, a C-pillar 2810,one or more door beams 2812, a cross car beam 2814, a front header 2816,a rear header 2818, a cow top 2820, a roof rail 2822, a lateral roof bow2824, longitudinal roof bow 2826, one or more body cross members 2828, abody cross member 2830, and/or rocker 2832.

Moreover, the structural components and/or cellular structures thereofin accordance with the present disclosure may be used as or form a partof vehicle underbody components, for example, as a rocker and/or one ormore underbody cross members. Also, the strengthening members inaccordance with the present disclosure may be used as or form a part ofvehicle engine compartment components, for example, as one or moreengine compartment cross members.

Further, cellular structures as disclosed herein may be incorporatedinto a vehicle structure as a supplement to the frame, a crash can,pillar, door, roof rail, hood, and/or rocker components of a vehicle inthe form of an impact energy absorber that is fitted inside, on oraround a frame, a crash can, pillar, door, roof rail, hood, and/or arocker component. For example in a Small Overlap Rigid Barrier (SORB)impact, a cellular structure may be fitted to the outside and/or insideof a front rocker and/or a hinge-pillar to absorb impact energy and toreduce the intrusions to the hinge pillar, rocker, front door, andpassenger compartment. In an oblique or perpendicular side pole impact,the cellular structure may be also fitted to the inside, on or around amiddle rocker, a middle frame, a side door, a B-pillar, or a roof rail,to absorb side impact energy and protect occupants by mitigating theintrusions to the side door and passenger compartment. In a pedestrianimpact, the cellular structure may be part of the hood outer or fittedunder the hood as a hood inner to absorb the impact energy and protectthe pedestrian. In a frontal impact, the cellular structure may be partof a front rail (a crash can for unitized vehicle) or fitted inside ofthe front rail (or crash can) to absorb the impact energy, minimize sidebending, improve deceleration pulse as well as to reduce the intrusionto the passenger compartment.

Additionally, cellular structures as disclosed herein may beincorporated in interior components of a vehicle. For example, cellularstructures may serve as a strengthening backing for a center console,HVAC system and air duct components, bumper trims, bumper energyabsorbers, hood inners, grill opening reinforcements, a utility box, armrests, door trims, pillar trims, lift-gate trims, interior panel trims,instrument panel trims, and head liners.

Depending on the application, cells of embodiments of the presentdisclosure will have varied shapes (i.e. various cross sections) toaccommodate specific cellular structure and structural component spaceconstraints. When used as a vehicle front rail, for example, to achieveoptimized axial crush performance, the lengths and/or thicknesses of thesides can be tuned to provide optimal strength, size and shape to meetengine compartment constraints.

Further modifications and alternative embodiments of various aspects ofthe present teachings will be apparent to those skilled in the art inview of this description.

It is to be understood that the particular examples and embodiments setforth herein are non-limiting, and modifications to structure,dimensions, materials, and methodologies may be made without departingfrom the scope of the present teachings.

In particular, those skilled in the art will appreciate that a cellularstructure may include more than one section or portion, with eachsection or portion having one or more of the variations of the cellularstructures taught in accordance with the present disclosure. Saidvariation(s) can be made continuously or intermittently along the lengthof each longitudinal section. In other words, cellular structures thatembody combinations of one or more of the above variations to thedisclosed tunable parameters, which have not been illustrated orexplicitly described, are also contemplated. Additionally, a structuralcomponent may include more than one of the cellular structures inaccordance with the present disclosure disposed adjacent or spaced apartfrom one another therein.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the devices and methods ofthe present disclosure without departing from the scope of itsteachings. Other embodiments of the disclosure will be apparent to thoseskilled in the art from consideration of the specification and practiceof the teachings disclosed herein. It is intended that the specificationand embodiments described herein be considered as exemplary only.

For the purposes of this specification and appended claims, unlessotherwise indicated, all numbers expressing quantities, percentages, orproportions, and other numerical values used in the specification andclaims, are to be understood as being modified in all instances by theterm “about,” to the extent they are not already so modified.Accordingly, unless indicated to the contrary, the numerical parametersset forth in the following specification and attached claims areapproximations that may vary depending upon the desired propertiessought to be obtained. At the very least, and not as an attempt to limitthe application of the doctrine of equivalents to the scope of theclaims, each numerical parameter should at least be construed in lightof the number of reported significant digits and by applying ordinaryrounding techniques.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the present teachings are approximations, thenumerical values set forth in the specific examples are reported asprecisely as possible. Any numerical value, however, inherently containscertain errors necessarily resulting from the standard deviation foundin their respective testing measurements. Moreover, all ranges disclosedherein are to be understood to encompass any and all sub-ranges subsumedtherein.

It is noted that, as used in this specification and the appended claims,the singular forms “a,” “an,” and “the,” and any singular use of anyword, include plural referents unless expressly and unequivocallylimited to one referent. As used herein, the term “include” and itsgrammatical variants are intended to be non-limiting, such thatrecitation of items in a list is not to the exclusion of other likeitems that can be substituted or added to the listed items.

What is claimed is:
 1. A structural component comprising: a wallsurrounding a component interior space; and a first cellular structurepositioned within the component interior space, wherein the firstcellular structure includes a plurality of cells each having atwelve-cornered cross section including twelve sides and twelve cornerscreating nine internal angles and three external angles, wherein atleast two of the twelve sides have different cross-sectional lengths. 2.The structural component of claim 1, wherein: a first internal angle ofthe nine internal angles is approximately 140 degrees; and a secondinternal angle of the nine internal angles is approximately 110 degrees.3. The structural component of claim 1, wherein each of the sides of thetwelve-cornered cross section has substantially the same thickness. 4.The structural component of claim 3, wherein a ratio of a thickness ofthe sides to a length of the sides of the cross section ranges fromabout 1:4 to about 1:10,000.
 5. The structural component of claim 1,further including a second cellular structure at least partiallyoverlying or underlying the first cellular structure.
 6. The structuralcomponent of claim 5, wherein a cross section of each of the cells ofthe plurality of cells of the first cellular structure have a firstshape and a cross section of each of a plurality of cells of the secondcellular structure have a second shape.
 7. The structural component ofclaim 6, wherein the first shape and the second shape are differentshapes.
 8. The structural component of claim 6, wherein each of thefirst shape and the second shape have twelve corners and twelve sides.9. The structural component of claim 5, further including a platebetween the first cellular structure and the second cellular structure.10. The structural component of claim 1, wherein the structuralcomponent is, or forms at least a part of, a vehicle structural memberselected from the group consisting of: a crush can, a bumper, a fronthorn, a front rail, a front side rail, a rear side rail, a rear rail, aframe cross member, a shotgun, a hinge-pillar, an A-pillar, a B-pillar,a C-pillar, a door beam, a cross car beam, a front header, a rearheader, a cow top, a roof rail, a lateral roof bow, a roof panel, ahood, a hood inner, a longitudinal roof bow, a body cross member, a backpanel cross member, a rocker, an underbody cross member, an enginecompartment cross member, a roof panel, a door, a floor, a deck lid, alift gate, a trim backing, a battery protective housing, an oil pan, atransmission case, an intake manifold, a cylinder block, a strut mount,an engine mount, a transmission mount, a body shell, and a strengtheningrib of a casted or molded component.
 11. The structural component ofclaim 1, wherein the structural component is, or forms at least a partof, a shipping or packaging component selected from the group consistingof a shipping box, a pallet, and a cushioning member.
 12. The structuralcomponent of claim 1, wherein the structural component is, or forms atleast a part of, a rotor blade for a turbine.
 13. The structuralcomponent of claim 1, wherein the structural component is, or forms atleast a part of, a solar energy panel.
 14. The structural component ofclaim 1, wherein the structural component is, or forms at least a partof, an elongated board sport platform.
 15. A sandwich structurecomprising: first and second substantially planar structures; and acellular structure positioned between the first and second substantiallyplanar structures, the cellular structure including at least two cells,each cell including a plurality of longitudinal walls extending betweena top and a bottom of the cell, the longitudinal walls intersecting tocreate corners of the cell, wherein a transverse cross section of thecell includes at least two bisecting planes of symmetry, the transversecross section including twelve sides and twelve corners arranged tocreate nine internal angles and three external angles, at least two ofthe twelve sides having different cross-sectional lengths.
 16. Thesandwich structure of claim 15, wherein: a first internal angle of thenine internal angles is approximately 140 degrees; and a second internalangle of the nine internal angles is approximately 110 degrees.
 17. Thesandwich structure of claim 15, wherein each of the sides of thetransverse cross section has substantially the same thickness.
 18. Thesandwich structure of claim 17, wherein a ratio of a thickness of thesides to a length of the sides of the cross section ranges from about1:4 to about 1:10,000.
 19. The sandwich structure of claim 15, whereinthe sandwich structure is a part of a vehicle.
 20. The sandwichstructure of claim 19, wherein the vehicle is selected from the groupconsisting of: an automobile, an RV, an ATV, a motorcycle, a watercraft,an aircraft, a spacecraft, a railway vehicle, a tram vehicle, a highspeed rail vehicle, a magnetic levitation vehicle, and a hyperloopcapsule or vehicle.
 21. The sandwich structure of claim 15, wherein thesandwich structure is, or forms at least a part of, a shipping orpackaging component selected from the group consisting of a shippingbox, a pallet, and a cushioning member.
 22. The sandwich structure ofclaim 15, wherein the sandwich structure is, or forms at least a partof, a solar energy panel.
 23. The sandwich structure of claim 15,wherein the sandwich structure is, or forms at least a part of, anelongated board sport platform.